Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
On truth-table reducibility to SAT
Information and Computation
Exponential lower bounds for the pigeonhole principle
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
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
Arithmetic theories with prenex normal form induction
Arithmetic theories with prenex normal form induction
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This paper considers the relational versions of the surjective and multifunction weak pigeonhole principles for PV, Σb1 and Θb2-formulas. We show that the relational surjective pigeonhole principle for Θb2 formulas in S12 implies a circuit block-recognition principle which in turn implies the surjective weak pigeonhole principle for Σb1 formulas. We introduce a class of predicates corresponding to poly-log length iterates of polynomial-time computable predicates and show that over R22, the multifunction pigeonhole principle for such predicates is equivalent to an "iterative" circuit block-recognition principle. A consequence of this is that if R23 proves this circuit iteration principle then RSA is vulnerable to quasi-polynomial time attacks.