On polynomial-time Turing and many-one completeness in PSPACE

Watanabe, Osamu; Tang, Shouwen

doi:10.1016/0304-3975(92)90074-p

Cited by 13 publications

(2 citation statements)

References 12 publications

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“…Here also, it is of course not known whether this class differs from P and therefore an assumption is necessary. Assuming that either randomized completeness notions differ or that PSPACE has a set with a dense subset of high generalized Kolmogorov complexity, Watanabe and Tang [WT89] show that the many-one and Turing complete degrees differ on PSPACE. From recent work of Buhrman and Fortnow [BF96] it follows that there exists a relativized world in which the <^ and the <\ _ tt complete set on PSPACE differ.…”

Section: Degrees Of Complete Setsmentioning

confidence: 99%

Complete Sets and Structure in Subrecursive Classes

Buhrman¹,

Torenvliet²

1998

Logic Colloquium’ 96

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Section: Degrees Of Complete Setsmentioning

confidence: 99%

Complete Sets and Structure in Subrecursive Classes

Buhrman¹,

Torenvliet²

1998

Logic Colloquium’ 96

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“…Evidence for the plausibility of the CvKL conjecture as cited in [26] includes the following facts: The CvKL conjecture holds for E = DTIME(2 linear ) (Ko and Moore, [20]) and for NE (Watanabe [45], Buhrman, Homer, and Torenvliet [4]). Under certain additional hypotheses it holds for PSPACE (Watanabe and Tang [46]). If E = NE the CvKL conjecture holds for NP ∪ co-NP and if E = NE ∩ co-NE it holds for NP (Selman [36]).…”

Section: Introductionmentioning

confidence: 99%

Relative to a Random Oracle, NP Is Not Small

Kautz

Miltersen

1996

Journal of Computer and System Sciences

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Resource-bounded measure as originated by Lutz is an extension of classical measure theory which provides a probabilistic means of describing the relative sizes of complexity classes. Lutz has proposed the hypothesis that NP does not have p-measure zero, meaning loosely that NP contains a non-negligible subset of exponential time. This hypothesis implies a strong separation of P from NP and is supported by a growing body of plausible consequences which are not known to follow from the weaker assertion P = NP. It is shown in this paper that relative to a random oracle, NP does not have p-measure zero. The proof exploits the following independence property of algorithmically random sequences: if A is an algorithmically random sequence and a subsequence A 0 is chosen by means of a bounded Kolmogorov-Loveland

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Cook versus Karp-Levin: Separating completeness notions if NP is not small

Lutz

Mayordomo

1994

Lecture Notes in Computer Science

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Under the hypothesis that NP does not have p-measure 0 (roughly, that NP contains more than a negligible subset of exponential time), it is show n that there is a language that is polynomial-time Turing complete (``Cook complete''), but not polynomial-time many-one complete (``Karp-Levin complete''), for NP. This conclusion, widely believed to be true, is not known to follow from P<>NP or other traditional complexitytheoretic hypotheses. Evidence is presented that ``NP does not have p-measure 0'' is a reasonable hypothesis with many credible consequences. Additional such consequences proven here include the separation of many truth-table reducibilities in NP (e.g., k queries versus k+1 queries), the class separation E<>NE, and the existence of NP search problems that are not reducible to the corresponding decision problems. Disciplines Theory and Algorithms AbstractUnder the hypothesis that NP does not have p-measure 0 roughly, that NP contains more than a negligible subset of exponential time, it is show n that there is a language that is P T -complete Cook complete", but not P m -complete Karp-Levin complete", for NP. This conclusion, widely believed to be true, is not known to follow from P 6 = NP or other traditional complexity-theoretic hypotheses.Evidence is presented that NP does not have p-measure 0" is a reasonable hypothesis with many credible consequences. Additional such consequences proven here include the separation of many truthtable reducibilities in NP e.g., k queries versus k +1 queries, the class separation E 6 = NE, and the existence of NP search problems that are not reducible to the corresponding decision problems.

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On polynomial-time Turing and many-one completeness in PSPACE

Cited by 13 publications

References 12 publications

Complete Sets and Structure in Subrecursive Classes

Complete Sets and Structure in Subrecursive Classes

Relative to a Random Oracle, NP Is Not Small

Cook versus Karp-Levin: Separating completeness notions if NP is not small

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