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Complexity classes without machines: on complete languages for UP
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Relativizing relativized computations
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Locating P/poly optimally in the extended low hierarchy
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If NP has polynomial-size circuits, then MA=AM
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Improving known solutions is hard
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Computing Solutions Uniquely Collapses the Polynomial Hierarchy
SIAM Journal on Computing
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New Collapse Consequences of NP Having Small Circuits
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Symmetric alternation captures BPP
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STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
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Some connections between nonuniform and uniform complexity classes
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
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SCT '95 Proceedings of the 10th Annual Structure in Complexity Theory Conference (SCT'95)
On Some Central Problems in Computational Complexity
On Some Central Problems in Computational Complexity
Algebras of feasible functions
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Sparse Oracles And Uniform Complexity Classes
SFCS '84 Proceedings of the 25th Annual Symposium onFoundations of Computer Science, 1984
A Tight Karp-Lipton Collapse Result in Bounded Arithmetic
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
Nondeterministic Instance Complexity and Proof Systems with Advice
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
The 1-versus-2 queries problem revisited
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
A tight Karp-Lipton collapse result in bounded arithmetic
ACM Transactions on Computational Logic (TOCL)
Proof systems that take advice
Information and Computation
Complexity classes of equivalence problems revisited
Information and Computation
Parameterized complexity of eulerian deletion problems
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
Survey: The consequences of eliminating NP solutions
Computer Science Review
Clique cover and graph separation: new incompressibility results
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
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Via competing provers, we show that if a language A is self-reducible and has polynomial-size circuits then S"2^A=S"2. Building on this, we strengthen the Kamper-AFK theorem, namely, we prove that if NP@?(NP@?coNP)/poly then the polynomial hierarchy collapses to S"2^N^P^@?^c^o^N^P. We also strengthen Yap's theorem, namely, we prove that if NP@?coNP/poly then the polynomial hierarchy collapses to S"2^N^P. Under the same assumptions, the best previously known collapses were to ZPP^N^P and ZPP^N^P^^^N^^^P, respectively ([SIAM Journal on Computing 28 (1) (1998) 311; Journal of Computer and System Sciences 52 (3) (1996) 421], building on [Proceedings of the 12th ACM Symposium on Theory of Computing, ACM Press, New York, 1980, pp. 302-309; Journal of Computer and System Sciences 39 (1989) 21; Theoretical Computer Science 85 (2) (1991) 305; Theoretical Computer Science 26 (3) (1983) 287]). It is known that S"2@?ZPP^N^P [Proceedings of the 42nd IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Silver Spring, MD, 2001, pp. 620-629]. That result and its relativized version show that our new collapses indeed improve the previously known results. The Kamper-AFK theorem and Yap's theorem are used in the literature as bridges in a variety of results-ranging from the study of unique solutions to issues of approximation-and so our results implicitly strengthen those results.