On reductions of NP sets to sparse sets

Author

Homer, Steven ; Longpré, Luc

Author_Institution

Dept. of Comput. Sci., Boston Univ., MA, USA

fYear

1991

fDate

30 Jun-3 Jul 1991

Firstpage

79

Lastpage

88

Abstract

M. Ogiwara and O. Watanabe (1990) showed that if SAT is bounded truth-table reducible to a sparse set, then P=NP. In the present work, the authors simplify their proof, strengthen the result, and use it to obtain several new results. Among the new results are the following: applications of the main theorem to log-truth-table and log-Turing reductions of NP sets to sparse sets; generalizations of the main theorem which yield results similar to the main result at arbitrary levels of the polynomial hierarchy; and the construction of an oracle relative to which P≠NP but there are NP-complete sets which are f(n)-tt-reducible to a tally set, for any f(n)∈Ω(log n)

Keywords

Turing machines; computational complexity; set theory; NP-complete sets; P≠NP; P=NP; SAT; bounded truth-table reducible; log-Turing reductions; log-truth-table; oracle; polynomial hierarchy; sparse sets; tally set; Complexity theory; Computer science; Educational institutions; Encoding; History; Internet; Polynomials;

fLanguage

English

Publisher

ieee

Conference_Titel

Structure in Complexity Theory Conference, 1991., Proceedings of the Sixth Annual

Conference_Location

Chicago, IL

Print_ISBN

0-8186-2255-5

Type

conf

DOI

10.1109/SCT.1991.160246

Filename

160246