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Abstract: 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 k P , are "gap-definable," i.e., definable using the values of GapP functions alone. We show that there is a smallest... (Update)
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BibTeX entry: (Update)
S. Fenner, L. Fortnow, and S. Kurtz. Gap-definable counting classes. In Proceedings of the 6th IEEE Structure in Complexity Theory Conference, pages 30--42. IEEE, New York, 1991. http://citeseer.ist.psu.edu/fenner92gapdefinable.html More
@inproceedings{ fenner91gapdefinable,
author = "Stephen A. Fenner and Lance Fortnow and Stuart A. Kurtz",
title = "Gap-Definable Counting Classes",
booktitle = "Structure in Complexity Theory Conference",
pages = "30-42",
year = "1991",
url = "citeseer.ist.psu.edu/fenner92gapdefinable.html" }
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442 Concrete Mathematics (context) - Graham, Knuth et al. - 1989
291 Theoretical Computer Science (context) - Stockmeyer, hierarchy - 1977 ACM
251 The complexity of computing the permanent (context) - Valiant - 1979 DBLP
161 Recursively Enumerable Sets and Degrees (context) - Soare - 1987 ACM
126 PP is as hard as the polynomial-time hierarchy (context) - Toda - 1991 ACM DBLP
66 PP is closed under intersection - Beigel, Reingold et al. - 1991 ACM DBLP
55 On Some Central Problems in Computational Complexity (context) - Simon - 1975 ACM
53 Counting classes are at least as hard as the polynomial-time.. (context) - Toda, Ogiwara - 1992 ACM DBLP
44 the power of parity polynomial time (context) - Cai, Hemachandra - 1990
37 Counting classes: Thresholds (context) - Beigel, Gill - 1990
37 Counting classes: Thresholds (context) - Beigel, Gill et al. - 1990
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29 The complexity of sparse sets in P (context) - Allender - 1986 ACM DBLP
22 Turing machines with few accepting computations and low sets.. - Kobler, Schoning et al. - 1992 ACM DBLP
20 Computational complexity of probabilistic complexity classes (context) - Gill - 1977
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10 Graph Isomorphism is low for PP (context) - Kobler, Schoning et al. - 1992 ACM DBLP
7 The power of witness reduction (context) - Gupta - 1991 DBLP
7 Lecture Notes in Computer Science (context) - Papadimitriou, Zachos et al. - 1983
6 Applications of Kolmogorov complexity in the theory of compu.. (context) - Li, Vit'anyi - 1990
5 PP and the polynomial hierarchy (context) - Beigel - 1992
3 Strukturelle Komplexitat von Anzahlproblemen (context) - Kobler - 1989
2 Gap-definability as a closure property - Fenner, Fortnow et al. - 1992 ACM DBLP
2 Private communication (context) - Toda - 1990
1 the construction of parallel computers form various bases of.. (context) - Goldschlager, Parberry - 1986
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