A complexity theory for feasible closure properties
TLDR
In particular, the authors showed that subtraction is hard for the closure properties of #P, SpanP, OptP, and MidP, which is a general theory of complexity of closure properties.About:
This article is published in Journal of Computer and System Sciences.The article was published on 1993-06-01 and is currently open access. It has received 95 citations till now. The article focuses on the topics: Closure (mathematics) & Function (mathematics).read more
Citations
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Journal ArticleDOI
Relationships among $PL$, $\#L$, and the determinant
Eric Allender,Mitsunori Ogihara +1 more
TL;DR: A very simple proof of theorem of Jung is given, showing that probabilistic logspace-bounded (PL) machines lose none of their computational power if they are restricted to run in polynomial time.
Journal ArticleDOI
The satanic notations: counting classes beyond #P and other definitional adventures
TL;DR: The potentially "off-by-one" nature of the definitions of counting (#P versus #NP), difference, and unambiguous (UP versus UNP; FewP versus FewNP) classes are explored, and suggestions as to logical approaches in each case are made.
Proceedings ArticleDOI
Subtractive reductions and complete problems for counting complexity classes
TL;DR: It is shown that the main counting complexity classes #P, #NP, as well as all higher counting complexityclasses # ċ ΠkP, k ≥ 2, are closed under subtractive reductions, and problems that are complete for these classes via subtractive reduction are pursued.
Book
Counting complexity
TL;DR: In this paper, the authors survey the vast area of counting complexity, concentrating on a few of the most important results in the area, and present a survey of the literature in counting complexity.
Proceedings ArticleDOI
Relationships among PL, #L, and the determinant
Eric Allender,Mitsunori Ogihara +1 more
TL;DR: A very simple proof of a theorem of Jung (1985) is given, showing that probabilistic logspace-bounded (PL) machines lose none of their computational power if they are restricted to run in polynomial time.
References
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Book
Computers and Intractability: A Guide to the Theory of NP-Completeness
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
Book
Introduction to Automata Theory, Languages, and Computation
TL;DR: This book is a rigorous exposition of formal languages and models of computation, with an introduction to computational complexity, appropriate for upper-level computer science undergraduates who are comfortable with mathematical arguments.
Proceedings ArticleDOI
The complexity of theorem-proving procedures
TL;DR: It is shown that any recognition problem solved by a polynomial time-bounded nondeterministic Turing machine can be “reduced” to the problem of determining whether a given propositional formula is a tautology.
Journal ArticleDOI
The complexity of enumeration and reliability problems
TL;DR: For a large number of natural counting problems for which there was no previous indication of intractability, that they belong to the class of computationally eqivalent counting problems that are at least as difficult as the NP-complete problems.