On relativized exponential and probabilistic complexity classes
Information and Control
Almost optimal lower bounds for small depth circuits
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Algebraic methods in the theory of lower bounds for Boolean circuit complexity
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
With probability one, a random oracle separates PSPACE from the polynomial-time hierarchy
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
Journal of Computer and System Sciences
Indexing of subrecursive classes
STOC '78 Proceedings of the tenth 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
Parity, circuits, and the polynomial-time hierarchy
SFCS '81 Proceedings of the 22nd Annual Symposium on Foundations of Computer Science
Relativized circuit complexity
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Separating the polynomial-time hierarchy by oracles
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
On proving circuit lower bounds against the polynomial-time hierarchy: positive and negative results
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
| Hi-index | 0.00 |
We propose a model of computation where a Turing machine is given random access to an advice string With random access, an advice string of exponential length becomes meaningful for polynomially bounded complexity classes We compare the power of complexity classes under this model It gives a more stringent notion than the usual model of computation with relativization Under this model of random access, we prove that there exist advice strings such that the Polynomial-time Hierarchy PH and Parity Polynomial-time $\bigoplus$P all collapse to P Our main proof technique uses the decision tree lower bounds for constant depth circuits [Yao85, Cai86,Hås86]and the algebraic machinery of Razborov and Smolensky [Raz87, Smo87].