Circuit Value Problem

Boolean example circuit

The Circuit Value Problem (or Circuit Evaluation Problem) is the computational problem of computing the output of a given Boolean circuit on a given input.

The problem is complete for P under uniform AC⁰ reductions. Note that, in terms of time complexity, it can be solved in linear time simply by a topological sort.

The Boolean Formula Value Problem (or Boolean Formula Evaluation Problem) is the special case of the problem when the circuit is a tree. The Boolean Formula Value Problem is complete for NC¹.^[1]

The problem is closely related to the Boolean Satisfiability Problem which is complete for NP and its complement, the Propositional Tautology Problem, which is complete for co-NP.

See also

• Circuit satisfiability
• Switching lemma

References

1. Samuel R. Buss (Jan 1987). "The Boolean formula value problem is in ALOGTIME". In Alfred V. Aho (ed.). Proceedings of the 19th Annual ACM Symposium on Theory of Computing (STOC). ACM. pp. 123–131. doi:10.1145/28395.28409. (Author's draft)

• Richard E. Ladner (Jan 1975). "The circuit value problem is log space complete for P". ACM SIGACT News. 7 (101): 18–20. doi:10.1145/990518.990519.