On the construction of parallel computers from various bases of Boolean functions
Theoretical Computer Science
Complexity measures for public-key cryptosystems
SIAM Journal on Computing - Special issue on cryptography
SIAM Journal on Computing
Probalisitic complexity classes and lowness
Journal of Computer and System Sciences
Relativized counting classes: relations among thresholds, parity, and mods
Journal of Computer and System Sciences
Counting classes are at least as hard as the polynomial-time hierarchy
SIAM Journal on Computing
Symbolic Boolean manipulation with ordered binary-decision diagrams
ACM Computing Surveys (CSUR)
Turing machines with few accepting computations and low sets for PP
Journal of Computer and System Sciences
Gap-definable counting classes
Journal of Computer and System Sciences
Theoretical Computer Science
Upward separation for FewP and related classes
Information Processing Letters
Unambiguous Computation: Boolean Hierarchies and Sparse Turing-Complete Sets
SIAM Journal on Computing
The Complexity of Equivalence and Containment for Free Single Variable Program Schemes
Proceedings of the Fifth Colloquium on Automata, Languages and Programming
Counting Classes: Thresholds, Parity, Mods, and Fewness
STACS '90 Proceedings of the 7th Annual Symposium on Theoretical Aspects of Computer Science
Complexity of Problems on Graphs Represented as OBDDs (Extended Abstract)
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
Size and Variable Ordering of OBDDs Representing Treshold Functions
COCOON '97 Proceedings of the Third Annual International Conference on Computing and Combinatorics
Two remarks on the power of counting
Proceedings of the 6th GI-Conference on Theoretical Computer Science
Looking for an Analogue of Rice's Theorem in Circuit Complexity Theory
KGC '97 Proceedings of the 5th Kurt Gödel Colloquium on Computational Logic and Proof Theory
The Boolean isomorphism problem
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Hi-index | 0.00 |
One way of suggesting that an NP problem may not be NP-complete is to show that it is in the class UP. We suggest an analogous new approach--weaker in strength of evidence but more broadly applicable--to suggesting that concrete NP problems are not NP-complete. In particular we introduce the class EP, the subclass of NP consisting of those languages accepted by NP machines that when they accept always have a number of accepting paths that is a power of two. Since if any NP-complete set is in EP then all NP sets are in EP, it follows--with whatever degree of strength one believes that EP differs from NP--that membership in EP can be viewed as evidence that a problem is not NP-complete. We show that the negation equivalence problem for OBDDs (ordered binary decision diagrams [17,12]) and the interchange equivalence problem for 2-dags are in EP. We also show that for boolean negation [20] the equivalence problem is in EPNP, thus tightening the existing NPNP upper bound. We show that FewP [2], bounded ambiguity polynomial time, is contained in EP, a result that is not known to follow from the previous SPP upper bound. For the three problems and classes just mentioned with regard to EP, no proof of membership/containment in UP is known, and for the problem just mentioned with regard to EPNP, no proof of membership in UPNP is known. Thus, EP is indeed a tool that gives evidence against NP-completeness in natural cases where UP cannot currently be applied.