TY - GEN

T1 - A complexity theory for feasible closure properties

AU - Ogiwara, Mitsunori

AU - Hemachandra, Lane A.

N1 - Funding Information:
* Work done in part while at the Tokyo Institute of Technology. + Research supported in part by the National Science Foundation under Grants NSF-INT-9116781/JSPS-ENG-207, CCR-8957604, and CCR-8996198 and by the International Information Science Foundation under Grant 90-l-3-228.

PY - 1991

Y1 - 1991

N2 - 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.

AB - 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.

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M3 - Conference contribution

AN - SCOPUS:0026373298

SN - 0818622555

T3 - Proc 6 Annu Struct Complexity Theor

SP - 16

EP - 29

BT - Proc 6 Annu Struct Complexity Theor

PB - Publ by IEEE

T2 - Proceedings of the 6th Annual Structure in Complexity Theory Conference

Y2 - 30 June 1991 through 3 July 1991

ER -