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This is a branch that includes: computational complexity theory; complexity classes, NP-completeness and other completeness concepts; oracle analogues of complexity classes; complexity-theoretic computational models; regular languages; context-free languages; Komolgorov Complexity and so on.

4 votes

An Alternative to the Cook-Levin Theorem

Yes, for example TMSAT (Turing Machine SAT): TMSAT = $\{ \langle \alpha, x, 1^n, 1^t \rangle : \exists u \in \{0,1\}^n$ such that $M_\alpha$ outputs 1 on input $\langle x,u \rangle$ within $t$ steps. …
Emil's user avatar
  • 726
0 votes

What is the relationship between "translation" and time complexity?

Your question reminded me of matroid problems. With these it is of great importance to specify how the input is given, as translating between input forms can increase the size of the input exponential …
Emil's user avatar
  • 726
2 votes
2 answers
361 views

Decision problem restricted to inputs that satisfy some necessary condition.

Consider the following decision problem: Problem 1 INPUT: A graph G. OUTPUT: YES if G is 3-colorable, NO if not. This is a well-known NP-complete problem. Now suppose that we have a necessary (but n …