Disjoint NP-Pairs and Propositional Proof Systems
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منابع مشابه
Tuples of Disjoint NP-Sets
Disjoint NP-pairs are a well studied complexity-theoretic concept with important applications in cryptography and propositional proof complexity. In this paper we introduce a natural generalization of the notion of disjoint NP-pairs to disjoint k-tuples of NP-sets for k ≥ 2. We define subclasses of the class of all disjoint k-tuples of NP-sets. These subclasses are associated with a proposition...
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We prove that every disjoint NP-pair is polynomial-time, many-one equivalent to the canonical disjoint NP-pair of some propositional proof system. Therefore, the degree structure of the class of disjoint NP-pairs and of all canonical pairs is identical. Secondly, we show that this degree structure is not superficial: Assuming there exist P-inseparable disjoint pairs, there exist intermediate di...
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For a propositional proof system P we introduce the complexity class DNPP(P ) of all disjoint NP-pairs for which the disjointness of the pair is efficiently provable in the proof system P . We exhibit structural properties of proof systems which make canonical NP-pairs associated with these proof systems hard or complete for DNPP(P ). Moreover, we demonstrate that non-equivalent proof systems c...
متن کاملClasses of representable disjoint NP-pairs
For a propositional proof system P we introduce the complexity class DNPP(P) of all disjoint NP-pairs for which the disjointness of the pair is efficiently provable in the proof system P . We exhibit structural properties of proof systems which make canonical NP-pairs associated with these proof systems hard or complete for DNPP(P). Moreover, we demonstrate that nonequivalent proof systems can ...
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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 ...
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We investigate the connection between propositional proof systems and their canonical pairs. It is known that simulations between proof systems translate to reductions between their canonical pairs. We focus on the opposite direction and study the following questions. Q1: Where does the implication [can(f) ≤ m can(g) ⇒ f ≤s g] hold, and where does it fail? Q2: Where can we find proof systems of...
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