Cook reducibility is faster than Karp reducibility in NP

Cook Reducibility is Faster than Karp Reduciblity in NP

Ground Reducibility is EXPTIME-Complete

We prove that ground reducibility is EXPTIME-complete in the general case. EXPTIME-hardness is proved by encoding the computations of an alternating Turing machine whose space is polynomially bounded. It is more difficult to show that ground reducibility belongs to DEXPTIME. We associate first an automaton with disequality constraints AR;t to a rewrite system R and a term t. This automaton is d...

Cook Versus Karp-Levin: Separating Completeness Notions if NP Is not Small (Extended Abstract)

Under the hypothesis that NP does not have p-measure 0 (roughly, that NP contains more than a negligible subset of exponential time), it is show n that there is a language that is P T -complete (\Cook complete"), but not P m -complete (\Karp-Levin complete"), for NP. This conclusion, widely believed to be true, is not known to follow from P 6= NP or other traditional complexity-theoretic hypoth...

On Reducibility and Symmetry of Disjoint NP-Pairs

We consider some problems about pairs of disjoint NP sets. The theory of these sets with a natural concept of reducibility is, on the one hand, closely related to the theory of proof systems for propositional calculus, and, on the other, it resembles the theory of NP completeness. Furthermore, such pairs are important in cryptography. Among others, we prove that the Broken Mosquito Screen pair ...

Reducibility in Finite Posets

All the posets/lattices considered here are finite with element 0. An element x of a poset satisfying certain properties is deletable if P − x is a poset satisfying the same properties. A class of posets is reducible if each poset of this class admits at least one deletable element. When restricted to lattices, a class of lattices is reducible if and only if one can go from any lattice in this ...