form of the First Incompleteness Theorem is an easy consequence of the undecidability of the halting problem. This weaker form differs from the standard statement...

Look up undecidable or undecidability in Wiktionary, the free dictionary. Undecidable may refer to: Undecidable problem in computer science and mathematical...

represent the same object or not. For undecidability in axiomatic mathematics, see List of statements undecidable in ZFC. The halting problem (determining...

word undecidable, the term independent is sometimes used instead of undecidable for the "neither provable nor refutable" sense. Undecidability of a statement...

undecidability of theories. If an essentially undecidable theory T is interpretable in a consistent theory S, then S is also essentially undecidable....

- a poetic proof of undecidability of the halting problem animated movie - an animation explaining the proof of the undecidability of the halting problem...

Description numbers play a key role in many undecidability proofs, such as the proof that the halting problem is undecidable. In the first place, the existence...

In mathematics, a conjecture is a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis or...

solved. Inference in both Horn clause logic and first-order logic is undecidable, and therefore intractable. However, backward reasoning with Horn clauses...

JSTOR 2371045. Reprinted in The Undecidable, p. 89ff. The first expression of "Church's Thesis". See in particular page 100 (The Undecidable) where he defines the...

An impossible object (also known as an impossible figure or an undecidable figure) is a type of optical illusion that consists of a two-dimensional figure...

Julien; Halava, Vesa; Harju, Tero; Nicolas, Francois (2014). "Tighter Undecidability Bounds for Matrix Mortality, Zero-in-the-Corner Problems, and More"...

Journal of Symbolic Logic 5(2):56–68 (1940) Huet, Gérard P. (1973). "The Undecidability of Unification in Third Order Logic". Information and Control. 22 (3):...

is consistent. A statement is independent of ZFC (sometimes phrased "undecidable in ZFC") if it can neither be proven nor disproven from the axioms of...

halt. The undecidability of the halting problem (the problem of testing whether a Turing machine eventually halts) then implies the undecidability of Wang's...

in all finite models. Trakhtenbrot's theorem shows that this is also undecidable. Some notations: S a t ( Φ ) {\displaystyle {\rm {{Sat}(\Phi )}}} means...

accordingly. Some of the most important problems in mathematics are undecidable, e.g. the halting problem. The field of computational complexity theory...

This defines a metalanguage stack of increasing capability to resolve undecidability in the autonomous lower levels. If someone near process level needs...

problem and the Entscheidungsproblem it is often used in proofs of undecidability. Let A {\displaystyle A} be an alphabet with at least two symbols. The...

not decidable. This first such set, used by Berger in his proof of undecidability, required 20,426 Wang tiles. Berger later reduced his set to 104, and...

prove from T that σ is false. Sometimes, σ is said (synonymously) to be undecidable from T. (This concept is unrelated to the idea of "decidability" as in...

undecidable, but the various Turing machines figuring in the proof of the undecidability of the general halting problem all have as component a hypothetical...

natural number in a finite number of steps. A set is noncomputable (or undecidable) if it is not computable. A subset S {\displaystyle S} of the natural...

paper on undecidability" (Davis 1952:39), as well as Gödel's own extensions of and commentary on the topic. This appears as On Undecidable Propositions...

extended to show that deciding whether a CFG is inherently ambiguous is undecidable, by reduction to the Post correspondence problem. It can also show that...

theorem: undecidability in language theory (cf Hopcroft and Ullman p. 205ff and reference on p. 401 ibid: Greibach [1963] "The undecidability of the ambiguity...

of Peano arithmetic or not. Hence, PA is an example of an undecidable theory. Undecidability arises already for the existential sentences of PA, due to...

Metamathematics is the study of mathematics itself using mathematical methods. This study produces metatheories, which are mathematical theories about...

Turing, right from the start of his work, had as his goal a proof of the undecidability of the Entscheidungsproblem. He told me that the 'main idea' of the...

like Peano arithmetic, is incomplete and undecidable in the sense of Gödel. Robinson's work on undecidability culminated in his coauthoring Tarski et al...

be used to show that Q is incomplete and undecidable. This indicates that the incompleteness and undecidability of PA cannot be blamed on the only aspect...

that input. Given two CFGs, do they generate the same language? The undecidability of this problem is a direct consequence of the previous: it is impossible...

List of undecidable problems Spectral gap, in mathematics Cubitt, Toby S.; Perez-Garcia, David; Wolf, Michael M. (2015-12-10). "Undecidability of the spectral...

in NP. However, the opposite direction is not true: some problems are undecidable, and therefore even more difficult to solve than all problems in NP,...

mathematical logic Decidable problem and Undecidable problem Gödel's incompleteness theorem, a theorem on the undecidability of languages consisting of "true...

the origin, is selected as a halting state). Hooper, P. (1966). "The undecidability of the Turing machine immortality problem". Journal of Symbolic Logic...

satisfiability is undecidable. More specifically, it is a co-RE-complete problem and therefore not semidecidable. This fact has to do with the undecidability of the...

superposition or quantum entanglement. Problems that are undecidable using classical computers remain undecidable using quantum computers. What makes quantum algorithms...

every program, nor false for every program. The theorem generalizes the undecidability of the halting problem. It has far-reaching implications on the feasibility...

Wisconsin-Madison Scientific career Fields Mathematics, Logic Thesis On the Undecidability of Certain Finite Theories  (1967) Doctoral advisor Howard Jerome Keisler...

equation and always determine whether it has a solution in integers. The undecidability of the halting problem and the Diophantine problem has a number of implications...

1093/oso/9780195080308.003.0010. Rose, H. E. (1961). "On the consistency and undecidability of recursive arithmetic". Zeitschrift für Mathematische Logik und Grundlagen...

the Lincoln Laboratory. Berger's work on tiling was published as "The Undecidability of the Domino Problem" in the Memoirs of the AMS in 1966. This paper...

did research on the interface between algebra and logic, focusing on undecidability in group theory. At the time of her death, she was emeritus faculty...

Section 2.2: Pushdown Automata, pp.101–114. Jeffrey Kegler, "Perl and Undecidability Archived 17 August 2009 at the Wayback Machine", The Perl Review. Papers...

power over classical computers. Thus, quantum computers cannot solve undecidable problems like the halting problem, and the existence of quantum computers...

greatest importance. Namely, it would obviously mean that in spite of the undecidability of the Entscheidungsproblem, the mental work of a mathematician concerning...

problems in physics List of unsolved problems in mathematics List of undecidable problems List of NP-complete problems List of PSPACE-complete problems...

of the principle was given by Stephen Wolfram in February 1985. In Undecidability and Intractability in Theoretical Physics, Wolfram wrote that "[U]niversal...

Principia Mathematica und verwandter Systeme (called in English "On Formally Undecidable Propositions of Principia Mathematica and Related Systems"). In that...

ISBN 0-8186-2230-X. S2CID 40441974. Huet, Gérard P. (1 April 1973). "The undecidability of unification in third order logic". Information and Control. 22 (3):...

main result is that it is undecidable to test whether a cellular automaton is reversible, but he also shows the undecidability of testing whether a Garden...

problem is undecidable. 1955 - Evertt William Beth develops semantic tableaux. 1958 - William Boone independently proves the undecidability of the uniform...

the existence of undecidable statements had been known since Gödel's incompleteness theorem of 1931, previous examples of undecidable statements (such...

about, assuming these are consistent. In fact, the undecidability of ST implies the undecidability of first-order logic with a single binary predicate...

proven by Haskell Curry. It was published in Curry's 1969 paper "The undecidability of λK-conversion". Hindley, J.R.; Seldin, J.P. (1986). Introduction...

algorithmically undecidable word problem. Indeed, it is fairly easy to construct a finitely generated recursively presented group with undecidable word problem...

compressed as possible (to reduce overfitting). Planning in POMDP is undecidable in general. However, some settings have been identified to be decidable...

Likewise, a reduction computing a noncomputable function can reduce an undecidable problem to a decidable one. As Michael Sipser points out in Introduction...

Theorist Of the Limits of Mathematics". The New York Times. p. B6. "Undecidability of First-Order Logic" (PDF). Church, A. (1936). "An unsolvable problem...

instances as well. Some deep results of computational theory concern the undecidability of this question in many important cases. In computer algebra one often...

problem by first showing that the halting problem for Turing machines is undecidable: it is not possible to decide algorithmically whether a Turing machine...

This fragment is often preferred to MTL because some problems that are undecidable for MTL become decidable for MITL. A MITL formula is an MTL formula,...

In mathematics, Richardson's theorem establishes the undecidability of the equality of real numbers defined by expressions involving integers, π, ln ⁡...

of Authority’”, Derrida emphasizes the relation between decision and undecidability, and the tension between normativity and singularity. This interpretation...

Decidability of first-order monadic predicate logic (Leopold Löwenheim 1915) Undecidability of first-order predicate logic (Church's theorem 1936) Other important...

analysis indicates that some optimization problems are NP-complete, or even undecidable. Also, producing perfectly optimal code is not possible since optimizing...

"reasonable" properties of finitely presentable groups are algorithmically undecidable. The theorem is due to Sergei Adyan (1955) and, independently, Michael...

undecidability. He showed that the Post correspondence problem (PCP) of satisfying their constraints is, in general, undecidable. The undecidability of...

the mathematician Raphael Douady, he called the problem statistical undecidability (Douady and Taleb, 2010). Taleb has described his main challenge as...

Publications, Mineola, NY, 2003. Davis, Martin, ed. (1965), The Undecidable, Basic Papers on Undecidable Propositions, Unsolvable Problems And Computable Functions...

prototiles are seen on the list of aperiodic sets of tiles. The underlying undecidability of the domino problem implies that there exists no systematic procedure...

2022-01-23. Retrieved 2022-01-23. Feferman, Solomon (1998). "Deciding the undecidable: Wrestling with Hilbert's problems" (PDF). In the Light of Logic. Logic...

Robinson, in a 1971 paper which simplified Berger's techniques and undecidability proof, used this technique to obtain an aperiodic set of just six prototiles...

Colorado, Boulder. pp. 49–52. Kurtz, Stuart A.; Simon, Janos (2007). "The undecidability of the generalized Collatz problem". In Cai, J.-Y.; Cooper, S. B.; Zhu...

of paradoxes Self-reference Halting problem – the usual proof of its undecidability uses a similar contradiction Barile, Margherita. "Crocodile's Dilemma...

techniques, finite-state machines, Turing machines, Markov processes, and undecidability. Booth studied at the University of Connecticut, where he received his...

algorithmic implementations are guaranteed to terminate with an answer, or undecidable, meaning that they may never terminate. By bounding the scope of possibilities...

(unstable, unbalanced, not measurable), and anepikrita (unjudged, unfixed, undecidable). Therefore, neither our sense-perceptions nor our doxai (views, theories...

of violation of a specification on the final result of a program) is undecidable: there is no mechanical method that can always answer truthfully whether...

are newcomers to the book. Some readers see the book as oscillating undecidably between these alternatives, like the Rubin vase (a drawing that may be...

the meaning of the pre-defined (RDF or OWL) vocabulary. OWL Full is undecidable, so no reasoning software is able to perform complete reasoning for it...

2008. and "Perl is Undecidable". The Perl Review. 5: 7–11. Fall 2008., available online at Kegler, Jeffrey. "Perl and Undecidability". Archived from the...

computers". Scientific American. pp. 98–106. Berger, Robert (1966). "The undecidability of the domino problem". Memoirs of the American Mathematical Society...

arithmetic Tarski's undefinability theorem Church-Turing theorem of undecidability Löb's theorem Löwenheim–Skolem theorem Lindström's theorem Craig's theorem...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

answered by computation; more technically, that some decision problems are "undecidable" in the sense that there is no single algorithm that infallibly gives...

time itself may not be predictable by a halting program, due to the undecidability of the halting problem. In response, Tegmark notes that a constructive...

be computable. Moreover, the equality of two computable numbers is an undecidable problem. Some constructivists accept the existence of only those reals...

surprising being that almost all axiomatic systems can generate certain undecidable statements not provable within the system. The definition of a formal...

may therefore execute arbitrary programs. By the halting problem it is undecidable whether an arbitrary program executed in the Game of Life would ever...

single binary relation symbol to monadic logic, however, results in an undecidable logic. The formal system described above is sometimes called the pure...

is homeomorphic to another fixed simplicial complex. The problem is undecidable for complexes of dimension 5 or more. An abstract simplicial complex...

Nei Y.; Castro, Paulo A. L. (2025). "Machines that halt resolve the undecidability of artificial intelligence alignment". Scientific Reports. 15 (1): 15591...

JSTOR 2273508, S2CID 46061318 Harrington, L.; Shelah, S. (1982), "The undecidability of the recursively enumerable degrees", Bull. Amer. Math. Soc. (N.S...

(1923–2016), Swiss-American group theorist and logician, expert on undecidability in group theory Annette Huber-Klawitter (born 1967), German algebraic...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

Intuitionism (with respect to Brouwer). Martin Davis (ed.) (1965), The Undecidable, Raven Press, Hewlett, NY. Compilation of original papers by Gödel, Church...

are true or false. Many problems in mathematics have been shown to be undecidable after these initial examples were established. In 1947, Markov and Post...

[UK]: Acumen. pp. 108–109. ISBN 978-1-84465-409-3. OCLC 715184861. Undecidability and the ten modes As part of his Pyrrhonian revival Aenesidemus assembled...

However, type inference in System F (without explicit type annotations) is undecidable. Under the Curry–Howard isomorphism, System F corresponds to second-order...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

Quarterly, vol. 19, no.3 (Spring 1982), pp. 239–255. Geary, Edward A. "Undecidability in Joyce's 'The Sisters,'" Studies in Short Fiction, vol. 26 (Summer...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

anyone interested in modern set theory. On the Question of Absolute Undecidability, Philosophia Mathematica (III) 14 (2006) On Reflection Principles, Annals...

2000. ISBN 9780393322293. Davis, Martin (2004). The Undecidable : Basic papers on undecidable propositions, unsolvable problems and computable functions...

Neumann suggested to Gödel that he should try to transform his results for undecidable propositions about integers. Less than a month later, von Neumann communicated...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

forcing arguments. With PCF theory, he showed that in spite of the undecidability of the most basic questions of cardinal arithmetic (such as the continuum...

ISBN 978-0-387-74640-1 Kurtz, Stuart A.; Simon, Janos (2007). "The Undecidability of the Generalized Collatz Problem". In Cai, Jin-Yi; Cooper, S. Barry;...

time itself may not be predictable by a halting program, due to the undecidability of the halting problem. He also explicitly discusses the more restricted...

if any, are not applied to enough arguments to be simplified. It is undecidable whether a general combinatory term has a normal form; whether two combinatory...

Problems in Mathematics", in Davis, Martin (ed.), The undecidable. Basic papers on undecidable propositions, unsolvable problems and computable functions...

(6)/\operatorname {SO} (5)=\operatorname {SU} (3)/\operatorname {SU} (2)} ⁠. It is undecidable whether a given ⁠ n {\displaystyle n} ⁠-dimensional manifold is homeomorphic...

Stephen Cole Kleene used a third value to represent predicates that are "undecidable by [any] algorithms whether true or false" As with bivalent logic, truth...

Handbook of Proof Theory. North-Holland: 476–546. Alfred Tarski, Andrzej Mostowski, and Raphael Robinson (1953) Undecidable Theories. North-Holland. v t e...

that case. The satisfiability problem for monadic second-order logic is undecidable in general because this logic subsumes first-order logic. The monadic...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

{\displaystyle R} ⁠ can be of any complexity class, or it can even be an undecidable problem such as the halting problem. If another problem ⁠ R ′ {\displaystyle...

to handle using OOP's concept of inheritance. Behavioral subtyping is undecidable in general, so it cannot be easily implemented by a compiler. Because...

it is an undecidable problem to determine, given a finite presentation of a group, whether the group is Hopfian. Unlike the undecidability of many properties...

May 28 - Alan Turing submits "On Computable Numbers", proving the undecidability of the Halting problem and the decision problem for logic. Computer...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

general, undecidable in Turing's original paper. Rice's theorem shows that any non-trivial question about the output of a Turing machine is undecidable. A universal...

arbitrary Turing machine, determining whether it is a decider is an undecidable problem. This is a variant of the halting problem, which asks for whether...

disproof of Goldbach's conjecture must exist (the conjecture may be undecidable in traditional ZF set theory). Thus to Brouwer, we are not justified...

which are sometimes called Culik–Yu classes; membership in these proved undecidable. Wolfram's class 2 can be partitioned into two subgroups of stable (fixed-point)...

is also the first question in ordinary mathematics proved undecidable in ZFC; Undecidable even if ZFC is augmented by taking the generalized continuum...

assumptions about language, and in so doing dictates a statement about undecidability, the difficulties inherent in totalization, their own readability, or...

comes at a price when the type inferences (and other properties) become undecidable, and when more attention must be paid by the programmer to annotate code...

disproved from these axioms. In this sense, the continuum hypothesis is undecidable, and it is the most widely known example of a natural statement that...

that a given expression is non-zero, or of showing that the problem is undecidable. For example, if x1, ..., xn are real numbers, then there is an algorithm...

whether a given program will ever halt or will run forever; this is the undecidability of the halting problem. As long as the system is responsive, infinite...

propositions are known as formally undecidable propositions. For example, the continuum hypothesis is undecidable in the Zermelo–Fraenkel set theory as...

termination, type argument inference, and ambiguous programs. In general it is undecidable whether a Java program using generics is well-typed or not, so any type...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

Church proved additional undecidability results, showing that both Peano arithmetic and first-order logic are undecidable. Later work by Emil Post and...

from them—even though the abstraction may simply yield a result of undecidability. For instance, students in a class may be abstracted by their minimal...

this poset is a lattice. The theory of this lattice is known to be an undecidable problem. Similarly, the set of all computably enumerable vector spaces...

expression language from its grammar. Furthermore, it is algorithmically undecidable whether the language recognized by a parsing expression grammar is empty...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

shortly after this positive result, Kurt Gödel published On Formally Undecidable Propositions of Principia Mathematica and Related Systems (1931), showing...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

formalism for real-time systems. Full MTL over infinite timed words is undecidable. The full metric temporal logic is defined similarly to linear temporal...

about it. Known results include: The rank problem is algorithmically undecidable for the class of all finitely presented groups. Indeed, by a classical...

Meanwhile on Earth Annick Jérémy Clapin Mr. K Tallulah H. Schwab Night Call Greg Michiel Blanchart 2025 Undecidable Professor Abraham Emanuele Bosco Short...

NP-complete, the SMT problem is typically NP-hard, and for many theories it is undecidable. Researchers study which theories or subsets of theories lead to a decidable...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

then one would be able to solve computational problems known to be undecidable in computer science. These results concern infinite systems, finite systems...

elementary theories of various algebraic structures. He showed the undecidability of the elementary theory of finite groups, of free nilpotent groups...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

1090/s0002-9904-1965-11354-4. MR 0199177. Ax, James (1965). "On the undecidability of power series fields". Proceedings of the American Mathematical Society...

Press, ISBN 0-19-853189-3. Martin Davis, ed. (1965). The Undecidable – Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions...

"in-between bits, the judders and rumbles and low howls drifting somewhere undecidable between composed music and sound design ... the un-music, the audiable...

might contain the solution to the halting problem or some other Turing-undecidable problem. Such an infinite tape of data is called a Turing oracle. Even...

called non-computable or undecidable. An extension of the halting problem is called Rice's theorem, which states that it is undecidable (in general) whether...

provided us with the right preconceptions. Weinberg believed that any undecidability in mathematics, such as the continuum hypothesis, could be potentially...

and God", in Driessen, Alfred; Suarez, Antoine (eds.), Mathematical Undecidability, Quantum Nonlocality and the Question of the Existence of God, Dordrecht:...

the foundations of mathematics, with the timeline Computability and Undecidability. Second edition. Wadsworth/Thomson Learning, Belmont, CA, 2000. W. A...

special case of superinformation. Calculating Space Computability theory Undecidable problem Quantum circuit Generalized probabilistic theory Heaven, Douglas...

more generally, a set of EDs), and, if it terminates (which is a priori undecidable), output an instance that does satisfy the EGDs. An important subclass...

programs. This problem is a superset of the halting problem, which is undecidable. The same is true for unit testing. Additionally, unit testing by definition...

is to decide whether it halts or runs forever. The halting problem is undecidable in the general case, and naturally understanding the behaviour of a computer...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

that a natural generalization of the Collatz problem is algorithmically undecidable. Related to that, he developed the esoteric programming language FRACTRAN...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

unsolved problems List of lemmas List of theorems List of statements undecidable in ZFC Weisstein, Eric W. (2002). CRC Concise Encyclopedia of Mathematics...

{\displaystyle A} is provable. If a theory with the disjunction property has undecidable propositions, the excluded middle disjunctions of some excluded middle...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

whether it is homeomorphic to a given geometric object. This problem is undecidable for any d-dimensional manifolds for d ≥ 5 {\displaystyle d\geq 5} . Abstract...

false, while according to anti-realism, there is a third option for undecidable sentences that can be neither verified nor falsified. Knowledge is an...

proper (i.e. P ⊊ {\displaystyle \subsetneq } P/poly) because there are undecidable problems that are in P/poly. P/poly turns out to have a number of properties...

elected in 2012 Chauvenet Prize: the 2011 winner, for his article "Undecidability in number theory" Miller Research Professorship – University of California...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

Shore, R. (1993). "The theories of the T, tt, and wtt r.e. degrees: undecidability and beyond". In Univ. Nac. del Sur, Bahía Blanca (ed.). Proceedings...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

concepts may be paradoxical or self-undermining, rendering their meaning undecidable. To extend this notion, deconstruction and the practice of sous rature...

minimization techniques, FSMs, Turing machines, Markov processes, and undecidability. Excellent treatment of Markov processes pp. 449ff. Discusses Z-transforms...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

Publishers. pp. 137–160. Davis, Martin, ed. (1965). The Undecidable, Basic Papers on Undecidable Propositions, Unsolvable Problems And Computable Functions...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

(reciprocal mode). According to the mode deriving from dispute, we find that undecidable dissension about the matter proposed has come about both in ordinary...

See temporal modal logic. Church's theorem A theorem establishing the undecidability of certain decision problems in logic, such as the Entscheidungsproblem...

dependent types type checking remains decidable, but type inference becomes undecidable. Dependent ML has been superseded by ATS and is no longer under active...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

determining if there exists a LL(k) parser for some k that recognizes it is undecidable. For each k, there is a language that cannot be recognized by an LL(k)...

Kurt Gödel described the representing function in his 1934 paper "On undecidable propositions of formal mathematical systems" (the symbol "¬" indicates...

with Saharon Shelah and Jonathan Stavi). In database theory, the first undecidability result of the consequence problem for database dependencies (with Ashok...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

parameter types and covariance of the return type. Behavioural subtyping is undecidable in general: if q is the property "method for x always terminates", then...

states that for all non-trivial properties of partial functions, it is undecidable whether a Turing machine computes a partial function with that property...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

92. Tarski, Alfred (1953), "I: A General Method in Proofs of Undecidability", Undecidable Theories, Studies in Logic and the Foundations of Mathematics...

cellular automaton with a larger number of states; however, because of the undecidability of reversibility for non-block cellular automata, there is no computable...

p. 130. Kleene 1952, p. 46. Gödel, Kurt (2022) [1962]. On Formally Undecidable Propositions of Principia Mathematica and Related Systems. Translated...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

shows that whether polyominoes from a given set can tile the plane is undecidable, by mapping sets of Wang tiles to sets of polyominoes. Because the general...

the stranger as the person who is present yet unfamiliar, society's undecidable. In Modernity and Ambivalence Bauman attempted to give an account of...

Determining whether a callable has a side effect is difficult – indeed, undecidable by virtue of Rice's theorem. So, while this optimization is safe in a...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

algorithmically decided, and some semantic properties of programs are undecidable. Thus, even an indefinitely information-generating physical reality need...

ISBN 978-0-86171-396-7 Oha, Obododimma (2008), "Language, Exile, and the Burden of Undecidable Citizenship: Tenzin Tsundue and the Tibetan Experience", in Allatson...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

formalism say. Decision problems become harder to answer or completely undecidable. Formal language theory mostly studies formalisms to describe sets of...

syntactical incompleteness result in the introductory section of "On Formally Undecidable Propositions in Principia Mathematica and Related Systems I". The paradox...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

that this linguistic indeterminacy, or as J. Hillis Miller terms it, undecidability, places Carlyle as a perhaps unwilling and yet important contributor...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

accessed; determining the latter requires code analysis, and is in general undecidable. Syntactic garbage is a (usually strict) subset of semantic garbage,...

fragments, showing for instance that many expressive group STIT logics are undecidable or of high computational complexity. In the 2010s, STIT ideas were combined...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

refers to three "aporias": "the epoche of the rule", "the ghost of the undecidable", and "the urgency that obstructs the horizon of knowledge". Aporia is...

whether a set of Wang tiles forms a valid tessellation is undecidable, and its undecidability rests on finding sets of Wang tiles that can only tesselate...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

'communion.'" Judaism cloaked in Catholicism is one example of the undecidability of identity that influenced the thinker whom Cixous calls a "Jewish...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

arithmetic is also incomplete by Gödel's incompleteness theorem. In his 1953 Undecidable theories, Tarski et al. showed that many mathematical systems, including...

CRC Press, p. 233, ISBN 9781466513457. For more on this subject, see undecidable problem. Chomsky, Noam (Sep 1956). "Three models for the description...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

may not satisfy a set of EDs, and, if it terminates (which is a priori undecidable), output an instance that does satisfy the EDs. An embedded dependency...

always order a printing and a motion, right, left, or none" (footnote 12, Undecidable, p. 300) Like Turing, he defined erasure as printing a symbol "S0". And...

required/advisory) Third edition: 2012 (directives; rules, Decidable/Undecidable) MISRA compliance: 2016, updated 2020 MISRA C:2023 (MISRA C Third edition...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

pp. 161–172. Allowing equality tests between deeper nodes leads to undecidability. See: Tommasi, M. (1991). Automates d'Arbres avec Tests d'Égalités entre...

validate by textual analysis, that any text harbors inherent points of "undecidability" that undermine any stable meaning intended by the author. The process...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

Advancement of Science. Moore, Cristopher (1990), "Unpredictability and undecidability in dynamical systems", Physical Review Letters, 64 (20): 2354–2357,...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

undecidable for context-sensitive grammars, a fact that follows from the undecidability of the halting problem. It is, however, decidable for context-free grammars...

instead of justifying them. Skepticism – Knowledge is impossible or undecidable. Robert Fogelin claims to detect a suspicious resemblance between the...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

non-commutative) local ring is free. Sometimes, whether a module is free or not is undecidable in the set-theoretic sense. A famous example is the Whitehead problem...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

d'état… but whatever its origin, the truth is that we were animated by the undecidable decision that the provisional government would give the country the revolutionary...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

in number theory Function problem Model of computation Recursive set Undecidable problem Hunter, Geoffrey (1996) [1971]. "1.7: The notion of effective...

quotients: Regular language#Closure properties. Sheila Greibach (1963). "The undecidability of the ambiguity problem for minimal linear grammars". Information and...

Media. ISBN 978-981-4021-07-4. Svozil, Karl (1993). Randomness and Undecidability in Physics. WORLD SCIENTIFIC. Bibcode:1993rup..book.....S. doi:10.1142/1524...

considered a practical class for computing. Indeed, it contains every undecidable unary language, none of which can be solved in general by real computers...

from the original (PDF) on 2016-04-07. Huet, Gérard P. (1973). "The Undecidability of Unification in Third Order Logic". Information and Control. 22 (3):...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

concepts may be paradoxical or self-undermining, rendering their meaning undecidable Jacques Derrida, Paul de Man, J. Hillis Miller, Philippe Lacoue-Labarthe...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

poetry can be read as queer even if the question of her lesbianism is undecidable. In antiquity, Sappho's poetry was highly admired, and several ancient...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

{N} } ,+)) can interpret the true second-order arithmetic and is thus undecidable. Just as in first-order logic, second-order logic may include non-logical...

context-sensitive grammars (given a context-sensitive grammar G, is L(G)=∅ ?) is undecidable. Savitch has proven the following theoretical result, on which he bases...

(unstable, unbalanced, not measurable), and anepikrita (unjudged, unfixed, undecidable). Therefore, neither our sense-perceptions nor our doxai (views, theories...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

the London Mathematical Society, Series 2, Volume 42 (1937), p.230–265. Reprinted in M. Davis (ed.), The Undecidable, Raven Press, Hewlett, NY, 1965....

Hilbert-Bernays provability conditions do not obtain), one can construct formally undecidable (or even formally refutable) Henkin-sentences for the arithmetical system...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

A.; Schnoebelen, Ph. (1998). "Reset Nets Between Decidability and Undecidability". Proceedings of the 25th International Colloquium on Automata, Languages...

problem History of the Church–Turing thesis Lambda calculus List of undecidable problems Post correspondence problem Post's theorem Primitive recursive...

is that which constitutes a text in a particular way. The text is an undecidable (there is an inexistence of an effective or "strict" method of writing...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

technical logic terms such as tiyuvta "conclusive refutation" and tiqu "undecidable moot point", which are still used in Jewish legal writings, including...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

logic — (1987). Forever Undecided. ISBN 0192801414. puzzles based on undecidability in formal systems — (1992). Gödel's Incompleteness Theorems. New York:...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

about the existence of a finitely presented group with algorithmically undecidable word problem also substantially use HNN-extensions. The idea of HNN extension...

states that, for any nontrivial property P of partial functions, it is undecidable whether a given Turing machine computes a function with property P. The...

general to decide if two functions are extensionally equal due to the undecidability of equivalence from Church's theorem. The translation may apply the...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

possible that B is an undecidable problem for which no algorithm exists. M. Davis, ed., 1965. The Undecidable—Basic Papers on Undecidable Propositions, Unsolvable...

false by using the axioms. However, note that in some cases it may be undecidable if a statement can be proven or not. A model for an axiomatic system...

isomorphism in second homology is induced by some diffeomorphism. It is undecidable if a given 5-manifold is homeomorphic to S 5 {\displaystyle S^{5}} ,...

problem will require, and explain why some problems are intractable or undecidable. Solvable computational problems belong to complexity classes that define...

logical consequence of φ. Unlike propositional logic, first-order logic is undecidable (although semidecidable), provided that the language has at least one...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

mass gap (a special case of a spectral gap) in a system is known to be undecidable, meaning no computer algorithm exists that can find the answer programmatically...

used this device to prove that even in those more powerful systems, undecidability is still present. Turing's oracle machines are mathematical abstractions...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

is most often applied to hardware designs. For software, because of undecidability (see computability theory) the approach cannot be fully algorithmic...

In computability and complexity theory, ALL is the class of all decision problems. ALL contains all of the complex classes of decision problems, including...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

these four domains one performs a 'generic procedure', which in its undecidability is necessarily experimental, and one potentially recasts the situation...

2023. Retrieved 27 August 2023. Riebel, Johannes (March 2023). The Undecidability of BB(748): Understanding Gödel's Incompleteness Theorems (PDF) (Bachelor's...

can express both multiplication and addition, the resulting theory is undecidable. If we have an ordering predicate on natural numbers (less than, < {\displaystyle...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

eye that causes the story to hover between tragedy and farce. This undecidability is the symptom of the scale of the novel's address. Wright is that rare...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

In mathematics, constructive analysis is mathematical analysis done according to some principles of constructive mathematics. The name of the subject contrasts...

limit-computable, deterministic universes whose pseudo-randomness based on undecidable, Gödel-like halting problems is extremely hard to detect but does not...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

programming language theory. The equivalence of two lambda expressions is undecidable (but see unification (computer science)). This is also the case for the...

Classical Quarterly, 52 (2002): 248–56. Svavarsson, Svavar Hrafn, "Pyrrho's undecidable nature", Oxford Studies in Ancient Philosophy, 27 (2004): 249–295. Library...

distinction between parsing and execution, and makes syntax analysis an undecidable problem in these languages, meaning that the parsing phase may not finish...

a free play but from the necessity of analysis. Derrida called these undecidables—that is, unities of simulacrum—"false" verbal properties (nominal or...

Her dissertation showed that the theory of the rational numbers was an undecidable problem, by demonstrating that elementary number theory could be defined...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

1090/s0025-5718-1992-1146835-5, JSTOR 2153078, MR 1146835 Poonen, Bjorn (2008), "Undecidability in number theory" (PDF), Notices of the American Mathematical Society...

is undecidable since this allows encoding of the undecidable theory of integers (see Richardson's theorem). Still, one can handle the undecidable case...

calculated. Specific instances cannot be given but this follows from the undecidability of the halting problem. For instance, if Goldbach's conjecture is true...

(1957, space science) Pyotr Novikov (1957, mathematics, for proving the undecidability of the word problem for groups) Sergei Prokofiev (1957, music, posthumously...

Banal Reality: Comparative Thoughts on Simulation and Concreteness". The Undecidable Unconscious: A Journal of Deconstruction and Psychoanalysis. 6 (1): 29–45...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

abstraction refinement, and barrier certificates. Most verification tasks are undecidable, making general verification algorithms impossible. Instead, the tools...

The decision problem of whether an arbitrary grammar is ambiguous is undecidable because it can be shown that it is equivalent to the Post correspondence...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

homeomorphism problem for 4-manifolds is undecidable. In addition, since even recognizing the trivial group is undecidable, it is not even possible in general...

computational irreducibility notes". A New Kind of Science. Wolfram, Stephen, "Undecidability and intractability in theoretical physics". Physical Review Letters...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

hence it is recursively enumerable. On the other hand, the problem is undecidable. Some other recursively enumerable languages that are not recursive include:...

the grammar. The latter problem is called the halting problem and is undecidable. Recursively enumerable languages are closed under Kleene star, concatenation...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

United States - Japan - Europe. Contradictions of the free market. The undecidable conflicts between protectionism and free trade. The unstoppable flow...

which generally means better performance. Reps, Thomas (2000-01-01). "Undecidability of context-sensitive data-dependence analysis". ACM Transactions on...

queries. Solving the boundedness problem on arbitrary Datalog programs is undecidable, but it can be made decidable by restricting to some fragments of Datalog...

Bałus, Wojciech (1994). "Dürer's 'Melencolia I': Melancholy and the Undecidable". Artibus et Historiae. 15 (30): 9–21. doi:10.2307/1483470. JSTOR 1483470...

Specifically, the algorithm cannot solve the constant problem, which is undecidable when it needs to determine whether an arbitrary complex number expression...

the above is that it is undecidable whether a (positive) range concatenation language is nonempty, because it is undecidable whether the intersection...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

Springer. ISBN 978-3-319-75620-2. de Acosta, Alejandro (2009). "Two undecidable questions for thinking in which anything goes". In Randall Amster (ed...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

difference is, that it becomes undecidable whether a specific function definition defines a μ-recursive function, as it is undecidable whether a computable (i...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

number that encodes the solution of the halting problem (or any other undecidable problem) according to a chosen encoding scheme. Chaitin's constant, Ω...

vulnerability. Due to many forms of static analysis being computationally undecidable, the mechanisms for performing it may not always terminate with the correct...

2386L. doi:10.1109/TIT.2006.874434. S2CID 1414385. Li, C. T. (2023). "Undecidability of Network Coding, Conditional Information Inequalities, and Conditional...

Ron Wood". Last.fm. 8 November 2024. Gorman, Clare (1 June 2015). The Undecidable: Jacques Derrida and Paul Howard. Cambridge Scholars Publishing. ISBN 9781443883597...

science, such as the variation of the proof that the halting problem is undecidable that uses Rice's Theorem. Due to security concerns regarding the Trusting...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

equal. Moreover, determining if ρ ≤ 1 {\displaystyle \rho \leq 1} is an undecidable problem. Nevertheless, in recent years much progress has been done on...

(complexity) NP-completeness NP-hardness EXPTIME PSPACE BPP (complexity) BQP Undecidable problem Halting problem Rice's theorem No free lunch theorem List of...

to believe in a god."" Alfred Driessen, Antoine Suarez, Mathematical undecidability, quantum nonlocality, and the question of the existence of God (1997)...

of validity in first-order logic on the class of all finite models is undecidable. In fact, the class of valid sentences over finite models is not recursively...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

x.x\bot } . Determining whether a term has a head normal form is an undecidable problem. Barendregt introduced a notion of an "effective" Böhm tree that...

known as the Church-Turing Thesis and proved that first-order logic is undecidable. 1962 Clark, Wesley A. Designed LINC, the first functional computer scaled...

Emperors (divus). The etymology of flamen remains obscure, and perhaps undecidable. The term is traditionally connected with the Proto-Germanic verb *blōtaną...

decide the question. This was historically the first problem for which undecidability could be proven. As usual for such a proof, computable means computable...

He used it to confirm Gödel by proving that the halting problem is undecidable. 1940 Edward Condon displayed Nimatron, a digital machine that played...

 29–122. Section 4.1: Decidable Languages, pp. 152–159. Section 5.1: Undecidable Problems from Language Theory, pp. 172–183. Elaine Rich (2008). Automata...

dependencies that can be inclusion dependencies or functional dependencies is undecidable by reduction from the word problem for monoids. Declarative referential...

of the halting problem is among the simplest, most-easily described undecidable decision problems: Given an arbitrary positive integer n and a list of...

Penguin Books. ISBN 0-14-01-4534-6. Gödel, Kurt (1992). On Formally Undecidable Propositions of Principia Mathematica and Related Systems (Reprint ed...

(PDF) from the original on 2012-03-07 Robinson, Raphael M. (1971), "Undecidability and nonperiodicity of tilings in the plane", Inventiones Mathematicae...

"poison"] actually do interpretive violence to what would otherwise remain undecidable." Whereas a straightforward view on Plato's treatment of writing (in...

{\displaystyle \beth _{\alpha }} can exist. (In that case, the existence is undecidable in ZFC and controlled by the Generalized Continuum Hypothesis.) Even...

LL}}-({\mbox{RE}}\cup {\mbox{co-RE}})} . Not only are these problems undecidable, but neither they nor their complement are recursively enumerable. In...

the Solar System 1970 May Of optical illusions, from figures that are undecidable to hot dogs that float 1970 Jun Elegant triangle theorems not to be found...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

Baker 1975, p. 90. Baker 1975, p. 86. Richardson, D. (1968). "Some Undecidable Problems Involving Elementary Functions of a Real Variable". Journal...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

Geoffrey K. (2000) "Scooping the loop snooper: An elementary proof of the undecidability of the halting problem". Mathematics Magazine 73.4 (October 2000), 319–320...

consisting of one rule with a linear left-hand side is undecidable. Termination is also undecidable for systems using only unary function symbols; however...

combined logic S4.1 (in fact, even K4.1) is canonical. In general, it is undecidable whether a given axiom is canonical. We know a nice sufficient condition:...

of Edinburgh, 1992. LFCS report ECS-LFCS-92-227. Gilles Dowek. The undecidability of typability in the lambda-pi-calculus. In M. Bezem, J.F. Groote (Eds...

existential (i.e. Σ 1 1 {\displaystyle {\Sigma }_{1}^{1}} ) MSO theory is undecidable if we allow predicates on both vertices and edges. Thus, in a sense,...

Giorgi Japaridze in 1992. Interpretability logic Tarski, Alfred (1953), Undecidable theories, Studies in Logic and the Foundations of Mathematics, Amsterdam:...

doi:10.1007/978-4-431-55639-8 Scholte, T. (2019). "Heuristics for the Undecidable." She Ji: The Journal of Design, Economics, and Innovation, 5(4), 379–382...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

ISBN 0-7923-6151-2, pages 221–230. Martin Davis, 1965. The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems, and Computable Functions...

10, no. 4 (2004). Accessed 21 August 2023. See article On Formally Undecidable Propositions of Principia Mathematica and Related Systems and Gödel 1931...

and God", in Driessen, Alfred; Suarez, Antoine (eds.), Mathematical Undecidability, Quantum Nonlocality and the Question of the Existence of God, Dordrecht:...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

Goldfarb showed that validity of formulas from the larger class was in fact undecidable. Grunwald–Wang theorem. Wilhelm Grunwald published an incorrect proof...

equality, which requires proof. As a consequence type checking becomes undecidable in extensional type theory because programs in the theory might not terminate...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

the equality of two real numbers given by an expression is known to be undecidable (specifically, real numbers defined by expressions involving the integers...

field of p-adic numbers (independently proven by J. Ax and S. Kochen), undecidability of the elementary theory of finite symmetric groups, decidability of...

is unreachable is at least as hard as the halting problem and hence undecidable Debray, Saumya K.; Evans, William; Muth, Robert; De Sutter, Bjorn (1...

of proofs. According to the mode deriving from dispute, we find that undecidable dissension about the matter proposed has come about both in ordinary...

equivalent to the axiom of choice (that is, their truth values in ZF, while undecidable, are the same as that of AC). The most important among them are Zorn's...

modulus of convergence is undecidable. In recursion theory, the limit lemma proves that it is possible to encode undecidable problems using limits. There...

Parys (2014) writes that this undecidability result is well known, and attributes it to Trahtenbrot (1950) on the undecidability of first-order satisfiability...

that this problem is undecidable; consequently, any word problem that has a reduction from this basic problem is likewise undecidable. Combinatorics on words...

LL(k) and LR(k) parsers, the problem of generating an LLR/LRR parser is undecidable unless one has constructed a regular partition upfront. But even the...

some impractical problems, including some undecidable problems such as the unary version of any undecidable problem. In 1999, Jin-Yi Cai and D. Sivakumar...

included in The Undecidable. The mathematics of Church, Rosser, and Kleene that appear as reprints of original papers in The Undecidable is carried further...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

answer to the program. If arbitrary propagation is allowed, reasoning is undecidable and the program will be infinite. Warded Datalog± overcomes this issue...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

Turing machine running an algorithm that terminates on all inputs. An undecidable problem is a problem that is not decidable. As noted above, every context-sensitive...

15-32). Svozil, K. (1990). The quantum coin toss-testing microphysical undecidability. Physics Letters A, 143(9), 433-437. Downing, K. L. (1992). A qualitative...

(termination proof) can never be fully automated, since the halting problem is undecidable. For example, successively searching through the positive integers (1...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

non-classical logic. Amongst his most notable accomplishments is the proof of undecidability of the relevance logic R. He published numerous scientific papers in...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

theoretical issues relevant to DNA biomollecules such nondeterminism and undecidability in self-assembly. Since the early 2000s, she has focused on the study...

respectively. He was awarded the Lenin Prize in 1957 for proving the undecidability of the word problem in groups. He received the Order of Lenin in 1961...

exists a finitely presented group G such that the word problem for G is undecidable. A different proof was obtained by Boone in a paper published in 1958...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

South, East, West }. Single-tape, multi-head Turing machine: In an undecidability proof of the "problem of tag", Minsky and Shepherdson and Sturgis described...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

THOG. For each of the other symbols, are they a) definitely a THOG, b) undecidable, or c) definitely not a THOG?" Presented in this form, the task is quite...

Springer-Verlag, ISBN 978-3-540-44085-7 Mostowski, Andrzej (1949), "An undecidable arithmetical statement" (PDF), Fundamenta Mathematicae, 36 (1), Institute...

Product Puzzle", which is not impossible -gry, a word puzzle List of undecidable problems, no algorithm can exist to answer a yes–no question about the...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

away all semantic properties irrelevant to the reasoning. Because of undecidability, sound, fully automated, and always terminating reasonings on/proofs/static...

problem for first-order logic is unsolvable and that first-order logic is undecidable (see Church's theorem). A great amount of later work in mathematics was...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

121–123. doi:10.1093/analys/23.6.121. Gödel, Kurt (1931). On Formally Undecidable Propositions of Principia Mathematica and Related Systems. Basic Books...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

(Adleman's theorem). It also contains some undecidable problems, such as the unary version of every undecidable problem, including the halting problem. Because...

which suggested an argument that the continuum hypothesis is either undecidable or false in the sense of mathematical platonism. Woodin criticizes this...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

provable formulas . . . ." (p. 72 in Martin Davis ed. The Undecidable: "Postscriptum" to "On Undecidable Propositions of Formal Mathematical Systems" appearing...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

contradicting the original assumption that C {\displaystyle C} is enumerable but undecidable. We also have Sacks's splitting theorem—Given an enumerable but not computable...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

(Casino Real), ed. Robin Mackay (Urbanomic, 2014): 813–846. "Decision and Undecidability of the Event in Being and Event I and II," trans. Alyosha Edlebi, Parrhesia...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

and Libidinal Dis-economy". Jared Russell, "Stiegler and the Clinic," Undecidable Unconscious: A Journal of Deconstruction and Psychoanalysis 2 (2015):...

conjecture is true. Kaplansky's conjecture is thus an example of a statement undecidable in ZFC. In 1953, Kaplansky proposed the conjecture that finite values...

to the construction of specific Diophantine equations for which it is undecidable whether they have a solution, or even if they do, whether they have a...

Verleden Tijd Florian Short film De Overkammer Archie Short film 2022 #No_Filter Tyler 2025 Undecidable (posthumous release) Arturo Reyes Short film...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

the halting problem for particular cases, since the general problem is undecidable. It provides a solution which is sound, meaning that when it states that...

are based on the model-theoretic (Herbrand) semantics of Datalog. The undecidability of entailment of DatalogZ motivates the definition of limit DatalogZ...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

economics entails Diophantine formalisms. These come with natural undecidabilities and uncomputabilities. In the face of this, [the] conjecture [is] that...

compelling evidence one way or another (i.e., the issue is "intellectually undecidable") both options must be "live hypotheses" for the relevant chooser (i...

dominant logic used by mathematicians. In 1931, Gödel published On Formally Undecidable Propositions of Principia Mathematica and Related Systems, which proved...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

concentration-based probability for which reaction will occur next) is undecidable. More specifically, a limited Turing machine can be simulated with arbitrarily...

given a description of a polynomial-time probabilistic machine, it is undecidable in general to determine if it recognizes a language in BPP. PP has natural...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

convergence. A famous source of computable undecidability - and in turn also of a broad range of undecidable propositions - is the predicate expressing...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

inequalities is undecidable. Ray tracing in 3-D optical systems with a finite set of rectangular reflective or refractive objects is undecidable. Ray tracing...

combined logic S4.1 (in fact, even K4.1) is canonical. In general, it is undecidable whether a given axiom is canonical. We know a nice sufficient condition:...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

Cairns, Hannah (2018). "Some Halting Problems for Abelian Sandpiles Are Undecidable in Dimension Three". SIAM Journal on Discrete Mathematics. 32 (4): 2636–2666...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

Entscheidungsproblem by first showing that the halting problem for Turing machines is undecidable: in general, it is not possible to decide algorithmically whether a given...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

type inference algorithms, which often came out to be NP-hard, if not undecidable with respect to termination. Thus the HM performs as well as the best...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

integration in terms of elementary functions Richardson's theorem: Undecidability of inequalities of real numbers formed out of a class of elementary...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

of evolutionary computation. This confirms the initial result about undecidability of natural evolution and evolutionary algorithms and processes. Evolutionary...

window Knightian uncertainty Outside Context Problem Russell's teapot Undecidable problem Wild card (foresight) Tacit knowledge Meno's paradox Kenneth...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

{\displaystyle {\mathsf {ZFC}}} remains unknown. List of statements undecidable in Z F C {\displaystyle {\mathsf {ZFC}}} Gelfand–Naimark theorem Akemann...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

The existence of ℵ 2 {\displaystyle \aleph _{2}} -Aronszajn trees is undecidable in ZFC: more precisely, the continuum hypothesis implies the existence...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

theoretical computer science, such as the proof that the halting problem is undecidable. Ken Thompson started development on Unix in 1968 by writing and compiling...

integration in terms of elementary functions Richardson's theorem – Undecidability of equality of real numbers Symbolic integration – Computation of an...

Ellis and Daniel Guevara, editors (Oxford University Press, 2012). "The Undecidability of the Second-Order Unification Problem" (PDF). Theoretical Computer...

Bounded Degree" 2021 Moritz Lichter and Jamie Tucker-Foltz 2022 Elena Di Lavore and Yoàv Montacute 2024 Søren Brinck Knudstorp "Relevant S is Undecidable"...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

ISSN 0956-7968. since the halting problem for the latter class was proven to be undecidable "What to know before debating type systems | Ovid [blogs.perl.org]"....

theory. Furthermore, under Field's nominalization, statements that are undecidable in standard set theory like the continuum hypothesis become statable...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

automata. The asymptotic behavior of these PDEs is therefore logically undecidable. With John David Crawford he showed that the orbits of three-dimensional...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

had managed to prove the undecidability of practically all non-trivial invariant group properties, including the undecidability of being isomorphic to a...

Intelligence in Medicine 1989; 1: 167–174. N.C.A. da Costa (with F.A. Doria), Undecidability and incompleteness in classical mechanics, International J. Theoretical...

the time hierarchy theorem. In computability theory, one of the basic undecidable problems is the halting problem: deciding whether a deterministic Turing...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

the word problem in group theory, which is known to be algorithmically undecidable. In fact, there is no algorithm for deciding whether a given manifold...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

Oha, Obododimma (2008-01-01), "Language, Exile and the Burden of Undecidable Citizenship: Tenzin Tsundue and the Tibetan Experience", Exile Cultures...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

conjunctive query) is known as the Datalog boundedness problem and is undecidable. Extensions of conjunctive queries capturing more expressive power include:...

answering that question. In modern terms, Hilbert's tenth problem is an undecidable problem. In a Diophantine equation, there are two kinds of variables:...

propositional linear logic with multiplicatives, additives, and exponentials) is undecidable, full affine logic is decidable. Affine logic forms the foundation of...

quintic equation algebraically. Also provably unsolvable are so-called undecidable problems, such as the halting problem for Turing machines. Some well-known...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

tasked with the inspection. The theoretical reason for this is the undecidability of the halting problem: there cannot exist some algorithm which determines...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

sharply with Gödel's and Turing's results about the incompleteness and undecidability of the first-order theory of the natural numbers (using addition and...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

in contrast to DL's open world assumption. Also, F-logic is generally undecidable,[citation needed] whereas the SHOIN description logic that Web Ontology...

"Deciding the undecidable," Nature vol. 352, pp. 664–665 (1991). I. Stewart, From Here to Infinity, Oxford (1996). Comments on the undecidability proof for...

earlier sections was decidable, adding the quantifiers makes the logic undecidable. So far, the quantified extensions are first-order: they distinguish...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...