The polynomial time hierarchy collapses if the Boolean hierarchy collapses
SIAM Journal on Computing
Bounded queries to SAT and the Boolean hierarchy
Theoretical Computer Science
Bounded arithmetic, propositional logic, and complexity theory
Bounded arithmetic, propositional logic, and complexity theory
New Collapse Consequences of NP Having Small Circuits
SIAM Journal on Computing
The Boolean Hierarchy and the Polynomial Hierarchy: A Closer Connection
SIAM Journal on Computing
On an optimal propositional proof system and the structure of easy subsets of TAUT
Theoretical Computer Science - Complexity and logic
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Feasibly constructive proofs and the propositional calculus (Preliminary Version)
STOC '75 Proceedings of seventh annual ACM symposium on Theory of computing
Some connections between nonuniform and uniform complexity classes
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Journal of Computer and System Sciences
Competing provers yield improved Karp-Lipton collapse results
Information and Computation
Logical Foundations of Proof Complexity
Logical Foundations of Proof Complexity
Proof systems that take advice
Information and Computation
Verifying proofs in constant depth
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Different approaches to proof systems
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Verifying proofs in constant depth
ACM Transactions on Computation Theory (TOCT)
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Cook and Krajíček have recently obtained the following Karp-Lipton collapse result in bounded arithmetic: if the theory PV proves NP⊆ P/poly, then the polynomial hierarchy collapses to the Boolean hierarchy, and this collapse is provable in PV. Here we show the converse implication, thus answering an open question posed by Cook and Krajíček. We obtain this result by formalizing in PV a hard/easy argument of Buhrman et al. [2003]. In addition, we continue the investigation of propositional proof systems using advice, initiated by Cook and Krajíček. In particular, we obtain several optimality results for proof systems using advice. We further show that these optimal systems are equivalent to natural extensions of Frege systems.