TY - JOUR

T1 - P-selective sets and reducing search to decision vs self-reducibility

AU - Hemaspaandra, Edith

AU - Naik, Ashish V.

AU - Ogihara, Mitsunori

AU - Selman, Alan L.

N1 - Funding Information:
* Funding for this research was provided by the National Science Foundation under Grant CCR-9002292.
Funding Information:
Research performed while visiting the Department of Computer Science, State University of New York at Buffalo, Jan. 1992 Dec. 1992 and while affiliated with the Department of Computer Science, University of Electro-Communications. Supported in part by the JSPS under Grant NSF-INT-9116781 JSPS-ENG-207.

PY - 1996/10

Y1 - 1996/10

N2 - We distinguish self-reducibility of a language L with the question of whether search reduces to decision for L. Results include: (i) If NE ≠ E, then there exists a set t in NP - P such that search reduces to decision for L, search does not nonadaptively reduce to decision for L and L is not self-reducible, (ii) If UE ≠ E, then there exists a language L ∈ UP - P such that search nonadaptively reduces to decision for L, but L is not self-reducible, (iii) If UE ∩ co-UE ≠ E, then there is a disjunctive self-reducible language L ∈ UP - P for which search does not nonadaptively reduce to decision. We prove that if NE ⊈ BPE, then there is a language L ∈ NP - BPP such that L is randomly self-reducible, not nonadaptively randomly self-reducible, and not self-reducible. We obtain results concerning trade-offs in multiprover interactive proof systems and results that distinguish checkable languages from those that are nonadaptively checkable. Many of our results are proven by constructing p-selective sets. We obtain a p-selective set that is not ≤ Ptt-equivalent to any tally language, and we show that if P = PP, then every p-selective set is ≤ PT-equivalent to a tally language. Similarly, if P = NP, then every cheatable set is ≤ Pm-equivalent to a tally language. We construct a recursive p-selective tally set that is not cheatable.

AB - We distinguish self-reducibility of a language L with the question of whether search reduces to decision for L. Results include: (i) If NE ≠ E, then there exists a set t in NP - P such that search reduces to decision for L, search does not nonadaptively reduce to decision for L and L is not self-reducible, (ii) If UE ≠ E, then there exists a language L ∈ UP - P such that search nonadaptively reduces to decision for L, but L is not self-reducible, (iii) If UE ∩ co-UE ≠ E, then there is a disjunctive self-reducible language L ∈ UP - P for which search does not nonadaptively reduce to decision. We prove that if NE ⊈ BPE, then there is a language L ∈ NP - BPP such that L is randomly self-reducible, not nonadaptively randomly self-reducible, and not self-reducible. We obtain results concerning trade-offs in multiprover interactive proof systems and results that distinguish checkable languages from those that are nonadaptively checkable. Many of our results are proven by constructing p-selective sets. We obtain a p-selective set that is not ≤ Ptt-equivalent to any tally language, and we show that if P = PP, then every p-selective set is ≤ PT-equivalent to a tally language. Similarly, if P = NP, then every cheatable set is ≤ Pm-equivalent to a tally language. We construct a recursive p-selective tally set that is not cheatable.

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U2 - 10.1006/jcss.1996.0061

DO - 10.1006/jcss.1996.0061

M3 - Article

AN - SCOPUS:0030263710

VL - 53

SP - 194

EP - 209

JO - Journal of Computer and System Sciences

JF - Journal of Computer and System Sciences

SN - 0022-0000

IS - 2

ER -