A complexity theory for feasible closure properties

Mitsunori Ogiwara, Lane A. Hemachandra

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

12 Scopus citations

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 - Dec 1 1991
EventProceedings of the 6th Annual Structure in Complexity Theory Conference - Chicago, IL, USA
Duration: Jun 30 1991Jul 3 1991

Publication series

NameProc 6 Annu Struct Complexity Theor

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

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