Very sparse leaf languages

Lance Fortnow, Mitsunori Ogihara

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag
Pages375-386
Number of pages12
Volume4162 LNCS
ISBN (Print)3540377913, 9783540377917
StatePublished - 2006
Externally publishedYes
Event31st International Symposium on Mathematical Foundations of Computer Science, MFCS 2006 - Stara Lesna, Slovakia
Duration: Aug 28 2006Sep 1 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4162 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other31st International Symposium on Mathematical Foundations of Computer Science, MFCS 2006
CountrySlovakia
CityStara Lesna
Period8/28/069/1/06

Fingerprint

Leaves
Polynomials
Polynomial Hierarchy
Polynomial time
Truth table
Turing
Upper and Lower Bounds
NP-complete problem
Inclusion
Language

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Fortnow, L., & Ogihara, M. (2006). Very sparse leaf languages. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4162 LNCS, pp. 375-386). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4162 LNCS). Springer Verlag.

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 proceedingConference contribution

Fortnow, L & Ogihara, M 2006, Very sparse leaf languages. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 4162 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4162 LNCS, Springer Verlag, pp. 375-386, 31st International Symposium on Mathematical Foundations of Computer Science, MFCS 2006, Stara Lesna, Slovakia, 8/28/06.
Fortnow L, Ogihara M. Very sparse leaf languages. In 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)).
Fortnow, Lance ; Ogihara, Mitsunori. / Very sparse leaf languages. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4162 LNCS Springer Verlag, 2006. pp. 375-386 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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