On polynomial-time truth-table reducibility of intractable sets to P-selective sets

Toda, Seinosuke

doi:10.1007/bf02090391

Cited by 59 publications

(41 citation statements)

References 31 publications

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“…Most crucially in terms of the study in this paper, Ko [Ko83] showed that they have low nonuniform complexity (P-sel ⊆ P/O(n 2 )). A few among the many other simplicity results known to hold are: Ko and Schöning [KS85] showed that all P-selective sets in NP are in the second level of the low hierarchy of Schöning [Sch83], and Allender and Hemachandra [AH92] showed that the Ko-Schöning result is the strongest lowness result for P-sel that holds with respect to all oracles; a long line of work starting with Selman [Sel79] and Toda [Tod91] (see also [Siv99] and the citations therein) has shown that no P-selective set can be NP-hard under ≤ p m or various other reductions unless P = NP; Naik and Selman [NS99] have shown that no P-selective set can be truth-table-hard for NP unless certain (intuitively unlikely) containments hold in the relationship between adaptive and nonadaptive queries to NP; and as a consequence of the work of Ko [Ko83] and Cai [Cai01] no P-selective set can be truth-table-hard for NP (or even Turing-hard for NP) unless the polynomial hierarchy collapses to S 2 , where S 2 is the symmetric alternation class of Canetti [Can96] and Russell and Sundaram [RS98]. Note that S 2 ⊆ ZPP NP ⊆ NP NP [Cai01], where ZPP as usual denotes expected polynomial time, so this is a very dramatic collapse.…”

Section: Introductionmentioning

confidence: 99%

Algebraic Properties for Selector Functions

Hemaspaandra¹,

Hempel²,

Nickelsen³

2004

SIAM J. Comput.

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The nondeterministic advice complexity of the P-selective sets is known to be exactly linear.Regarding the deterministic advice complexity of the P-selective sets-i.e., the amount of KarpLipton advice needed for polynomial-time machines to recognize them in general-the best current upper bound is quadratic [Ko83] and the best current lower bound is linear [HT96].We prove that every associatively P-selective set is commutatively, associatively P-selective. Using this, we establish an algebraic sufficient condition for the P-selective sets to have a linear upper bound (which thus would match the existing lower bound) on their deterministic advice complexity: If all P-selective sets are associatively P-selective then the deterministic advice complexity of the P-selective sets is linear. The weakest previously known sufficient condition was P = NP.We also establish related results for algebraic properties of, and advice complexity of, the nondeterministically selective sets.

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Section: Introductionmentioning

confidence: 99%

Algebraic Properties for Selector Functions

Hemaspaandra¹,

Hempel²,

Nickelsen³

2004

SIAM J. Comput.

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“…Lemma 1 [11] Let L be a P-selective language, and S be a finite set. There is a polynomial-time algorithm that orders S according to membership in S.…”

Section: Preliminariesmentioning

confidence: 99%

Robustness of PSPACE-complete sets

Pavan

Wang

2007

Information Processing Letters

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“…Using this approach, Toda [Tod91] showed that UP and PSPACE cannot have P-selective truth-table-hard sets unless P = UP and P = PSPACE. …”

Section: Questionmentioning

confidence: 99%

Open questions in the theory of semifeasible computation

Faliszewski¹,

Hemaspaandra²

2006

SIGACT News

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The study of semifeasible algorithms was initiated by Selman's work a quarter of century ago [Sel79,Sel81,Sel82]. Informally put, this research stream studies the power of those sets L for which there is a deterministic (or in some cases, the function may belong to one of various nondeterministic function classes) polynomial-time function f such that when at least one of x and y belongs to L, then f (x, y) ∈ L ∩ {x, y}. The intuition here is that it is saying: "Regarding membership in L, if you put a gun to my head and forced me to bet on one of x or y as belonging to L, my money would be on f (x, y)."In this article, we present a number of open problems from the theory of semifeasible algorithms. For each we present its background and review what partial results, if any, are known.

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On polynomial-time truth-table reducibility of intractable sets to P-selective sets

Cited by 59 publications

References 31 publications

Algebraic Properties for Selector Functions

Algebraic Properties for Selector Functions

Robustness of PSPACE-complete sets

Open questions in the theory of semifeasible computation

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