Abstract
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 ≤ P tt-equivalent to any tally language, and we show that if P = PP, then every p-selective set is ≤ P T-equivalent to a tally language. Similarly, if P = NP, then every cheatable set is ≤ P m-equivalent to a tally language. We construct a recursive p-selective tally set that is not cheatable.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 194-209 |
| Number of pages | 16 |
| Journal | Journal of Computer and System Sciences |
| Volume | 53 |
| Issue number | 2 |
| DOIs | |
| State | Published - Oct 1996 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Computational Theory and Mathematics
Cite this
P-selective sets and reducing search to decision vs self-reducibility. / Hemaspaandra, Edith; Naik, Ashish V.; Ogihara, Mitsunori; Selman, Alan L.
In: Journal of Computer and System Sciences, Vol. 53, No. 2, 10.1996, p. 194-209.Research output: Contribution to journal › Article
}
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.
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 ≤ P tt-equivalent to any tally language, and we show that if P = PP, then every p-selective set is ≤ P T-equivalent to a tally language. Similarly, if P = NP, then every cheatable set is ≤ P m-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 ≤ P tt-equivalent to any tally language, and we show that if P = PP, then every p-selective set is ≤ P T-equivalent to a tally language. Similarly, if P = NP, then every cheatable set is ≤ P m-equivalent to a tally language. We construct a recursive p-selective tally set that is not cheatable.
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UR - http://www.scopus.com/inward/citedby.url?scp=0030263710&partnerID=8YFLogxK
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 -