Talk:Constructible function
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Binary representation
From the article:
- In the second definition, f is called time-constructible, if there exists a Turing machine M which, given a string 1n, outputs the binary representation of f(n) in O(f(n)) time.
Why does the Turing machine need to output the binary representation of f(n)? Balcazar, Diaz, and Gabarro's Structural Complexity (ch. 2, pg. 45) notes:
- f is time constructible if and only if it can be computed in O(f) steps. Here "computed" means that there exists a machine that on input 1n prints out 1f(n) in at most steps.
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