TY - GEN

T1 - Very sparse leaf languages

AU - Fortnow, Lance

AU - Ogihara, Mitsunori

N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

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.

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U2 - 10.1007/11821069_33

DO - 10.1007/11821069_33

M3 - Conference contribution

AN - SCOPUS:33750045990

SN - 3540377913

SN - 9783540377917

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 375

EP - 386

BT - Mathematical Foundations of Computer Science 2006 - 31st International Symposium, MFCS 2006, Proceedings

PB - Springer Verlag

T2 - 31st International Symposium on Mathematical Foundations of Computer Science, MFCS 2006

Y2 - 28 August 2006 through 1 September 2006

ER -