A complexity theory for feasible closure properties

Mitsunori Ogihara, Lane A. Hemachandra

Research output: Chapter in Book/Report/Conference proceedingConference contribution

12 Citations (Scopus)

Abstract

The authors propose and develop a complexity theory of feasible closure properties. For each of the classes #P, SpanP, OptP, and MidP, they establish complete characterizations--in terms of complexity class collapses--of the conditions under which the class has all feasible closure properties. In particular, #P is P-closed if and only if PP = UP; SpanP is P-closed if and only if R-MidP is P-closed if and only if PPP = NP; and OptP is P-closed if and only if NP = co-NP. Furthermore, for each of these classes, the authors show natural operations--such as subtraction and division--to be hard closure properties, in the sense that if a class is closed under one of these, then it has all feasible closure properties. They also study potentially intermediate closure properties for #P. These properties--maximum, minimum, median, and decrement--seem neither to be possessed by #P nor to be #P-hard.

Original languageEnglish (US)
Title of host publicationProc 6 Annu Struct Complexity Theor
PublisherPubl by IEEE
Pages16-29
Number of pages14
ISBN (Print)0818622555
StatePublished - 1991
Externally publishedYes
EventProceedings of the 6th Annual Structure in Complexity Theory Conference - Chicago, IL, USA
Duration: Jun 30 1991Jul 3 1991

Other

OtherProceedings of the 6th Annual Structure in Complexity Theory Conference
CityChicago, IL, USA
Period6/30/917/3/91

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Ogihara, M., & Hemachandra, L. A. (1991). A complexity theory for feasible closure properties. In Proc 6 Annu Struct Complexity Theor (pp. 16-29). Publ by IEEE.

A complexity theory for feasible closure properties. / Ogihara, Mitsunori; Hemachandra, Lane A.

Proc 6 Annu Struct Complexity Theor. Publ by IEEE, 1991. p. 16-29.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Ogihara, M & Hemachandra, LA 1991, A complexity theory for feasible closure properties. in Proc 6 Annu Struct Complexity Theor. Publ by IEEE, pp. 16-29, Proceedings of the 6th Annual Structure in Complexity Theory Conference, Chicago, IL, USA, 6/30/91.
Ogihara M, Hemachandra LA. A complexity theory for feasible closure properties. In Proc 6 Annu Struct Complexity Theor. Publ by IEEE. 1991. p. 16-29
Ogihara, Mitsunori ; Hemachandra, Lane A. / A complexity theory for feasible closure properties. Proc 6 Annu Struct Complexity Theor. Publ by IEEE, 1991. pp. 16-29
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