Complexity measures for public-key cryptosystems
SIAM Journal on Computing - Special issue on cryptography
Oracles for structural properties: the isomorphism problem and public-key cryptography
Journal of Computer and System Sciences
Bounded arithmetic, propositional logic, and complexity theory
Bounded arithmetic, propositional logic, and complexity theory
On an optimal propositional proof system and the structure of easy subsets of TAUT
Theoretical Computer Science - Complexity and logic
On reducibility and symmetry of disjoint NP pairs
Theoretical Computer Science - Mathematical foundations of computer science
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Optimal proof systems imply complete sets for promise classes
Information and Computation
SIAM Journal on Computing
Canonical disjoint NP-pairs of propositional proof systems
Theoretical Computer Science
Classes of representable disjoint NP-pairs
Theoretical Computer Science
Tuples of Disjoint $\mathsf{NP}$-Sets
Theory of Computing Systems
Reductions between disjoint NP-Pairs
Information and Computation
Survey of disjoint NP-pairs and relations to propositional proof systems
Theoretical Computer Science
Logical closure properties of propositional proof systems
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
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This paper focuses on the deduction theorem for propositional logic. We define and investigate different deduction properties and show that the presence of these deduction properties for strong proof systems is powerful enough to characterize the existence of optimal and even polynomially bounded proof systems. We also exhibit a similar, but apparently weaker condition that implies the existence of complete disjoint NP-pairs. In particular, this yields a sufficient condition for the completeness of the canonical pair of Frege systems and provides a general framework for the search for complete NP-pairs.