On the construction of parallel computers from various bases of Boolean functions
Theoretical Computer Science
The complexity of sparse sets in P
Proc. of the conference on Structure in complexity theory
Probabilistic quantifiers and games
Journal of Computer and System Sciences - Structure in Complexity Theory Conference, June 2-5, 1986
SIAM Journal on Computing
The Boolean hierarchy I: structural properties
SIAM Journal on Computing
Theoretical Computer Science
Relativized counting classes: relations among thresholds, parity, and mods
Journal of Computer and System Sciences
Complexity classes defined by counting quantifiers
Journal of the ACM (JACM)
PP is as hard as the polynomial-time hierarchy
SIAM Journal on Computing
Counting classes are at least as hard as the polynomial-time hierarchy
SIAM Journal on Computing
Theoretical Computer Science
Counting classes: thresholds, parity, mods, and fewness
Theoretical Computer Science - Selected papers of the 7th Annual Symposium on theoretical aspects of computer science (STACS '90) Rouen, France, February 1990
A uniform approach to define complexity classes
Theoretical Computer Science
Turing machines with few accepting computations and low sets for PP
Journal of Computer and System Sciences
Probabilistic polynomials, AC0 functions and the polynomial-time hierarchy
STACS '91 Selected papers of the 8th annual symposium on Theoretical aspects of computer science
Gap-definable counting classes
Journal of Computer and System Sciences
Complexity classes and sparse oracles
Journal of Computer and System Sciences
A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
SIAM Journal on Computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Strengths and Weaknesses of Quantum Computing
SIAM Journal on Computing
SIAM Journal on Computing
Relativized worlds with an infinite hierarchy
Information Processing Letters
Information Processing Letters
Complexity limitations on Quantum computation
Journal of Computer and System Sciences
The complexity theory companion
The complexity theory companion
Polynomial-time quantum algorithms for Pell's equation and the principal ideal problem
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Relativized separation of EQP from PNP
Information Processing Letters
Quantum computation and quantum information
Quantum computation and quantum information
Two remarks on the power of counting
Proceedings of the 6th GI-Conference on Theoretical Computer Science
Information and Computation
On Some Central Problems in Computational Complexity
On Some Central Problems in Computational Complexity
On PP-Low Classes
Generic oracles and oracle classes
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
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We study the complexity of quantum complexity classes such as EQP, BQP, and NQP (quantum analogs of P, BPP, and NP, respectively) using classical complexity classes such as ZPP, WPP, and C=P. The contributions of this paper are threefold. First, via oracle constructions, we show that no relativizable proof technique can improve the best known classical upper bound for BQP (BQP@?AWPP [Journal of Computer and System Sciences 59(2) (1999) 240]) to BQP@?WPP and the best known classical lower bound for EQP (P@?EQP) to ZPP@?EQP. Second, we prove that there are oracles A and B such that, relative to A, coRP is immune to NQP and relative to B, BQP is immune to P^C^=^P. Extending a result of de Graaf and Valiant [Technical Report quant-ph/0211179, Quantum Physics (2002)], we construct a relativized world where EQP is immune to MOD"p"^"kP. Third, motivated by the fact that counting classes (e.g., LWPP, AWPP, etc.) are the best known classical upper bounds on quantum complexity classes, we study properties of these counting classes. We prove that WPP is closed under polynomial-time truth-table reductions, while we construct an oracle relative to which WPP is not closed under polynomial-time Turing reductions. The latter result implies that proving the equality of the similar appearing classes LWPP and WPP would require nonrelativizable proof techniques. We also prove that both AWPP and APP are closed under =