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
Acta Informatica
Probalisitic complexity classes and lowness
Journal of Computer and System Sciences
Counting classes: thresholds, parity, mods, and fewness
STACS 90 Proceedings of the seventh annual symposium on Theoretical aspects of computer science
PP is closed under intersection
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
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
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
Turing machines with few accepting computations and low sets for PP
Journal of Computer and System Sciences
Graph Isomorphism is Low for PP
STACS '92 Proceedings of the 9th Annual Symposium on Theoretical Aspects of Computer Science
Gap-Definability as a Closure Property
STACS '93 Proceedings of the 10th Annual Symposium on Theoretical Aspects of Computer Science
Two remarks on the power of counting
Proceedings of the 6th GI-Conference on Theoretical Computer Science
ACM SIGACT News
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
The complexity of matrix rank and feasible systems of linear equations (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Graph nonisomorphism has subexponential size proofs unless the polynomial-time hierarchy collapses
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Complexity of finite-horizon Markov decision process problems
Journal of the ACM (JACM)
The Complexity of Computing the Size of an Interval
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Games with a Uniqueness Property
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
The Inherent Dimension of Bounded Counting Classes
COCOON '98 Proceedings of the 4th Annual International Conference on Computing and Combinatorics
Analysis of Quantum Functions (Preliminary Version)
Proceedings of the 19th Conference on Foundations of Software Technology and Theoretical Computer Science
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
UMC '02 Proceedings of the Third International Conference on Unconventional Models of Computation
Restrictive Acceptance Suffices for Equivalence Problems
FCT '99 Proceedings of the 12th International Symposium on Fundamentals of Computation Theory
CIAC '00 Proceedings of the 4th Italian Conference on Algorithms and Complexity
The complexity of the characteristic and the minimal polynomial
Theoretical Computer Science - Mathematical foundations of computer science
Information and Computation
On TC/sup 0/, AC/sup 0/, and Arithmetic Circuits
CCC '97 Proceedings of the 12th Annual IEEE Conference on Computational Complexity
The complexity of tensor calculus
Computational Complexity
Separability and one-way functions
Computational Complexity
Theoretical Computer Science
On the complexity of simulating space-bounded quantum computations
Computational Complexity
Lower bounds and the hardness of counting properties
Theoretical Computer Science
Quantum and classical complexity classes: separations, collapses, and closure properties
Information and Computation
A common algebraic description for probabilistic and quantum computations
Theoretical Computer Science - Mathematical foundations of computer science 2004
LWPP and WPP are not uniformly gap-definable
Journal of Computer and System Sciences
Error-bounded probabilistic computations between MA and AM
Journal of Computer and System Sciences
Revisiting a limit on efficient quantum computation
Proceedings of the 44th annual Southeast regional conference
Languages polylog-time reducible to dot-depth 1/2
Journal of Computer and System Sciences
The Complexity of Tensor Circuit Evaluation
Computational Complexity
Comparing action descriptions based on semantic preferences
Annals of Mathematics and Artificial Intelligence
Quantum and classical complexity classes: Separations, collapses, and closure properties
Information and Computation
Randomness and completeness in computational complexity
Randomness and completeness in computational complexity
On the hardness of the noncommutative determinant
Proceedings of the forty-second ACM symposium on Theory of computing
Quantum computing and polynomial equations over the finite field Z2
Quantum Information & Computation
Comparing action descriptions based on semantic preferences
JELIA'06 Proceedings of the 10th European conference on Logics in Artificial Intelligence
Survey: The consequences of eliminating NP solutions
Computer Science Review
The Chain Method to Separate Counting Classes
Theory of Computing Systems
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The function class #P lacks an important closure property: it is not closed under subtraction. To remedy this problem, we introduce the function class GapP as a natural alternative to #P. GapP is the closure of #P under subtraction and has all the other useful closure properties of #P as well. We show that most previously studied counting classes, including PP, C"=P, and Mod"kP, are ''gap-definable,'' i.e., definable using the values of GapP functions alone. We show that there is a smallest gap-definable class, SPP, which is still large enough to contain Few. We also show that SPP consists of exactly those languages low for GapP, and thus SPP languages are low for any gap-definable class. These results unify and improve earlier disparate results of J. Cai and L. Hemachandra (Math. Systems Theory23, No. 2 (1990), 95-106) and J. Kobler et al. (J. Comput. System Sci.44, No. 2 (1992), 272-286). We show further that any countable collection of languages is contained in a unique minimum gap-definable class, which implies that the gap-definable classes form a lattice under inclusion. Subtraction seems necessary for this result, since nothing similar is known for the #P-definable classes.