Abstract
Unger studied the balanced leaf languages defined via polylogarithmically sparse leaf pattern sets. Unger shows that NP-complete sets are not polynomial-time many-one reducible to such balanced leaf language unless the polynomial hierarchy collapses to Θ2p and that Σ2p-complete sets are not polynomial-time bounded-truth-table reducible (respectively, polynomial-time Turing reducible) to any such balanced leaf language unless the polynomial hierarchy collapses to Δ2p (respectively, Σ4p). This paper studies the complexity of the class of such balanced leaf languages, which will be denoted by VSLL. In particular, the following tight upper and lower bounds of VSLL are shown: 1. coNP ⊆ VSLL ⊆ coNP/poly (the former inclusion is already shown by Unger). 2. coNP/1 ⊈ VSLL unless PH = Θ2p. 3. For all constant c > 0, VSLL ⊈ coNP/nc. 4. P/(log log(n) + O(1)) ⊆ VSLL. 5. For all h(n) = log log(n) +ω(1), P/h ⊈ VSLL.
| Original language | English (US) |
|---|---|
| Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
| Publisher | Springer Verlag |
| Pages | 375-386 |
| Number of pages | 12 |
| Volume | 4162 LNCS |
| ISBN (Print) | 3540377913, 9783540377917 |
| State | Published - 2006 |
| Externally published | Yes |
| Event | 31st International Symposium on Mathematical Foundations of Computer Science, MFCS 2006 - Stara Lesna, Slovakia Duration: Aug 28 2006 → Sep 1 2006 |
Publication series
| Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
|---|---|
| Volume | 4162 LNCS |
| ISSN (Print) | 03029743 |
| ISSN (Electronic) | 16113349 |
Other
| Other | 31st International Symposium on Mathematical Foundations of Computer Science, MFCS 2006 |
|---|---|
| Country | Slovakia |
| City | Stara Lesna |
| Period | 8/28/06 → 9/1/06 |
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ASJC Scopus subject areas
- Computer Science(all)
- Theoretical Computer Science
Cite this
Very sparse leaf languages. / Fortnow, Lance; Ogihara, Mitsunori.
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4162 LNCS Springer Verlag, 2006. p. 375-386 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4162 LNCS).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Very sparse leaf languages
AU - Fortnow, Lance
AU - Ogihara, Mitsunori
PY - 2006
Y1 - 2006
N2 - Unger studied the balanced leaf languages defined via polylogarithmically sparse leaf pattern sets. Unger shows that NP-complete sets are not polynomial-time many-one reducible to such balanced leaf language unless the polynomial hierarchy collapses to Θ2p and that Σ2p-complete sets are not polynomial-time bounded-truth-table reducible (respectively, polynomial-time Turing reducible) to any such balanced leaf language unless the polynomial hierarchy collapses to Δ2p (respectively, Σ4p). This paper studies the complexity of the class of such balanced leaf languages, which will be denoted by VSLL. In particular, the following tight upper and lower bounds of VSLL are shown: 1. coNP ⊆ VSLL ⊆ coNP/poly (the former inclusion is already shown by Unger). 2. coNP/1 ⊈ VSLL unless PH = Θ2p. 3. For all constant c > 0, VSLL ⊈ coNP/nc. 4. P/(log log(n) + O(1)) ⊆ VSLL. 5. For all h(n) = log log(n) +ω(1), P/h ⊈ VSLL.
AB - Unger studied the balanced leaf languages defined via polylogarithmically sparse leaf pattern sets. Unger shows that NP-complete sets are not polynomial-time many-one reducible to such balanced leaf language unless the polynomial hierarchy collapses to Θ2p and that Σ2p-complete sets are not polynomial-time bounded-truth-table reducible (respectively, polynomial-time Turing reducible) to any such balanced leaf language unless the polynomial hierarchy collapses to Δ2p (respectively, Σ4p). This paper studies the complexity of the class of such balanced leaf languages, which will be denoted by VSLL. In particular, the following tight upper and lower bounds of VSLL are shown: 1. coNP ⊆ VSLL ⊆ coNP/poly (the former inclusion is already shown by Unger). 2. coNP/1 ⊈ VSLL unless PH = Θ2p. 3. For all constant c > 0, VSLL ⊈ coNP/nc. 4. P/(log log(n) + O(1)) ⊆ VSLL. 5. For all h(n) = log log(n) +ω(1), P/h ⊈ VSLL.
UR - http://www.scopus.com/inward/record.url?scp=33750045990&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33750045990&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:33750045990
SN - 3540377913
SN - 9783540377917
VL - 4162 LNCS
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 375
EP - 386
BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PB - Springer Verlag
ER -