NP is as easy as detecting unique solutions
Theoretical Computer Science
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
Almost everywhere high nonuniform complexity
Journal of Computer and System Sciences
Measure, Stochasticity, and the Density of Hard Languages
SIAM Journal on Computing
Gap-definable counting classes
Journal of Computer and System Sciences
Journal of Computer and System Sciences
Theoretical Computer Science
The Complexity and Distribution of Hard Problems
SIAM Journal on Computing
Almost every set in exponential time is P-bi-immune
Theoretical Computer Science
Cook versus Karp-Levin: separating completeness notions if NP is not small
Theoretical Computer Science
Relative to a random oracle, NP is not small
Journal of Computer and System Sciences
NP-hard sets are superterse unless NP is small
Information Processing Letters
P = BPP if E requires exponential circuits: derandomizing the XOR lemma
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Complexity theory retrospective II
The quantitative structure of exponential time
Complexity theory retrospective II
Fine Separation of Average-Time Complexity Classes
SIAM Journal on Computing
Complete distributional problems, hard languages, and resource-bounded measure
Theoretical Computer Science
The zero-one law holds for BPP
Theoretical Computer Science
Separating NP-Completeness notions under strong Hypotheses
Journal of Computer and System Sciences
On pseudorandomness and resource-bounded measure
Theoretical Computer Science
Randomness vs time: derandomization under a uniform assumption
Journal of Computer and System Sciences
The Density of Weakly Complete Problems under Adaptive Reductions
SIAM Journal on Computing
Graph Nonisomorphism Has Subexponential Size Proofs Unless the Polynomial-Time Hierarchy Collapses
SIAM Journal on Computing
MAX3SAT is exponentially hard to approximate if NP has positive dimension
Theoretical Computer Science
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Improved Lowness Results for Solvable Black-box Group Problems
Proceedings of the 17th Conference on Foundations of Software Technology and Theoretical Computer Science
Query Order and NP-Completeness
COCO '99 Proceedings of the Fourteenth Annual IEEE Conference on Computational Complexity
Super-polynomial versus half-exponential circuit size in the exponential hierarchy
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Baire categories on small complexity classes and meager--comeager laws
Information and Computation
Martingale families and dimension in P
Theoretical Computer Science
Martingale families and dimension in p
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
| Hi-index | 5.23 |
Derandomization techniques are used to show that at least one of the following holds regarding the size of the counting complexity class SPP: 1. µp(SPP)=0. 2. PH ⊆ SPP. In other words, SPP is small by being a negligible subset of exponential time or large by containing the entire polynomial-time hierarchy. This addresses an open problem about the complexity of the graph isomorphism problem: it is not weakly complete for exponential time unless PH is contained in SPP. It is also shown that the polynomial-time hierarchy is contained in SPPNP if NP does not have p-measure 0.