Structural complexity 1
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
Nondeterministic Instance Complexity and Proof Systems with Advice
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
Does Advice Help to Prove Propositional Tautologies?
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Different approaches to proof systems
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
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Cook and Krají茂戮驴ek [9] have obtained the following Karp-Lipton result in bounded arithmetic: if the theory proves , then collapses to , and this collapse is provable in . Here we show the converse implication, thus answering an open question from [9]. We obtain this result by formalizing in a hard/easy argument of Buhrman, Chang, and Fortnow [3].In addition, we continue the investigation of propositional proof systems using advice, initiated by Cook and Krají茂戮驴ek [9]. In particular, we obtain several optimal and even p-optimal proof systems using advice. We further show that these p-optimal systems are equivalent to natural extensions of Frege systems.