Quantitative relativizations of complexity classes
SIAM Journal on Computing
Separating the polynomial-time hierarchy by oracles
Proc. 26th annual symposium on Foundations of computer science
Relativizing complexity classes with sparse oracles
Journal of the ACM (JACM)
Theoretical Computer Science
Some connections between nonuniform and uniform complexity classes
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
On some central problems in computational complexity.
On some central problems in computational complexity.
Relativizing complexity classes with sparse oracles
Journal of the ACM (JACM)
On hiding information from an oracle
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
The ismorphism conjecture fails relative to a random oracle
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Separating and collapsing results on the relativized probabilistic polynomial-time hierarchy
Journal of the ACM (JACM)
Simple characterizations of P(#P) and complete problems
Journal of Computer and System Sciences
Competing Provers Yield Improved Karp-Lipton Collapse Results
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Some connections between bounded query classes and non-uniform complexity
Information and Computation
Competing provers yield improved Karp-Lipton collapse results
Information and Computation
The Complexity of Power-Index Comparison
AAIM '08 Proceedings of the 4th international conference on Algorithmic Aspects in Information and Management
Note: The complexity of power-index comparison
Theoretical Computer Science
Manipulating the quota in weighted voting games
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Competing provers yield improved Karp-Lipton collapse results
Information and Computation
Manipulating the quota in weighted voting games
Artificial Intelligence
Collapsing recursive oracles for relativized polynomial hierarchies
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
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Questions about the polynomial-time hierarchy are studied. In particular, the questions, “Does the polynomial-time hierarchy collapse?” and “Is the union of the hierarchy equal to PSPACE?” are considered, along with others comparing the union of the hierarchy with certain probabilistic classes. In each case it is shown that the answer is “yes” if and only if for every sparse set S, the answer is “yes” when the classes are relativized to S if and only if there exists a sparse set S such that the answer is “yes” when the classes are relativized to S. Thus, in each case the question is answered if it is answered for any arbitrary sparse oracle set.Long and Selman first proved that the polynomial-time hierarchy collapses if and only if for every sparse set S, the hierarchy relative to S collapses. This result is re-proved here by a different technique.