Reducibility, randomness, and intractibility (Abstract)
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
On some polynomial time reducibilities.
On some polynomial time reducibilities.
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We prove that a class of functions (denoted by NPCPt), whose graphs can be accepted in non-deterministic polynomial time, can be evaluated in deterministic polynomial time if and only if &ggr;-reducibility is equivalent to polynomial time many-one reducibility. We also modify the proof technique used to obtain part of this result to obtain the stronger result that if every &ggr;-reduction can be replaced by a polynomial time Turing reduction then every function in NPCPt can be evaluated in deterministic polynomial time.