Talk:Constructible function

Binary representation

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 1^f(n) in at most $c\cdot f(n)$ steps.

Neilc 06:05, 2 February 2007 (UTC)