How Reductions to Sparse Sets Collapse The Polynomial-time Hierarchy : A Primer Part II : Restricted Polynomial-time Reduction s Paul Young * 1 Introductio n In Part I of this paper, [Yo-92], we gave simple proofs, in a uniform format, of the major known results relating how polynomial-time Turing reductions of SAT to sparse sets collapse the polynomial time hierarchy. ) As one example, if SAT is polynomial time Turing reducible to a sparse set, the n the polynomial time hierarchy collapses to E 2 n 112 . It has long been known that if SAT is reducible to a sparse set by more restrictive polynomial time reductions, then even more dramatic collapses of the polynomial-time hierarchy must occur . Recently, ([OW-91]), Ogiwara and Watanabe proved that if SAT <1tt S for some sparse set S, then P = NP, a result which subsumed all earlier results on polynomial-time bounded-truth-table an d many-one reductions of SAT to sparse sets . In this part of the paper, Part II, we now give simple proofs of the major known results (pr e 1992) on how bounded truth-table on conjunctive and disjunctive reductions of SAT to sparse set s collapse the
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How reductions to sparse sets collapse the polynomial-time hierarchy: a primer: Part II restricted polynomial-time reductions
Young, Paul
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, Volume 23 (4)
Association for Computing Machinery – Oct 1, 1992
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