Complexity measures for public-key cryptosystems
SIAM Journal on Computing - Special issue on cryptography
Bounded arithmetic, propositional logic, and complexity theory
Bounded arithmetic, propositional logic, and complexity theory
Some consequences of cryptographical conjectures for S12 and EF
Information and Computation - Special issue: logic and computational complexity
On the Structure of Polynomial Time Reducibility
Journal of the ACM (JACM)
On reducibility and symmetry of disjoint NP pairs
Theoretical Computer Science - Mathematical foundations of computer science
Optimal proof systems imply complete sets for promise classes
Information and Computation
Reductions between Disjoint NP-Pairs
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
SIAM Journal on Computing
Disjoint NP-pairs from propositional proof systems
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
Representable disjoint NP-Pairs
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
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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 propositional proof system and possess complete tuples which are defined from the proof system. In our main result we show that complete disjoint NP-pairs exist if and only if complete disjoint k-tuples of NP-sets exist for all k ≥ 2. Further, this is equivalent to the existence of a propositional proof system in which the disjointness of all k-tuples is shortly provable. We also show that a strengthening of this conditions characterizes the existence of optimal proof systems.