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92
Computing Solutions Uniquely Collapses the Polynomial Hierarchy
 SIAM Journal on Computing
, 1993
"... Is there a singlevalued NP function that, when given a satisfiable formula as input, outputs a satisfying assignment? That is, can a nondeterministic function cull just one satisfying assignment from a possibly exponentially large collection of assignments? We show that if there is such a nondeterm ..."
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Cited by 41 (25 self)
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Is there a singlevalued NP function that, when given a satisfiable formula as input, outputs a satisfying assignment? That is, can a nondeterministic function cull just one satisfying assignment from a possibly exponentially large collection of assignments? We show that if there is such a nondeterministic function, then the polynomial hierarchy collapses to its second level. As the existence of such a function is known to be equivalent to the statement "every multivalued NP function has a singlevalued NP refinement," our result provides the strongest evidence yet that multivalued NP functions cannot be refined. We prove our result via theorems of independent interest. We say that a set A is NPSVselective (NPMVselective) if there is a 2ary partial function in NPSV (NPMV, respectively) that decides which of its inputs (if any) is "more likely" to belong to A; this is a nondeterministic analog of the recursiontheoretic notion of the semirecursive sets and the extant complexitythe...
Computing functions with parallel queries in np, Theoretical Computer Science 141
 175–193. JID:ARTINT AID:2529 /FLA [m3G; v 1.47; Prn:29/09/2010; 11:04] P.30 (130) 30 P.E. Dunne et al. / Artificial Intelligence
, 1995
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PSelective Sets, and Reducing Search to Decision vs. SelfReducibility
, 1993
"... We obtain several results that distinguish selfreducibility of a language L with the question of whether search reduces to decision for L. These include: (i) If NE 6= E, then there exists a set L in NP \Gamma P such that search reduces to decision for L, search does not nonadaptively reduces to de ..."
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Cited by 40 (10 self)
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We obtain several results that distinguish selfreducibility of a language L with the question of whether search reduces to decision for L. These include: (i) If NE 6= E, then there exists a set L in NP \Gamma P such that search reduces to decision for L, search does not nonadaptively reduces to decision for L, and L is not selfreducible. Funding for this research was provided by the National Science Foundation under grant CCR9002292. y Department of Computer Science, State University of New York at Buffalo, 226 Bell Hall, Buffalo, NY 14260 z Department of Computer Science, State University of New York at Buffalo, 226 Bell Hall, Buffalo, NY 14260 x Research performed while visiting the Department of Computer Science, State University of New York at Buffalo, Jan. 1992Dec. 1992. Current address: Department of Computer Science, University of ElectroCommunications, Chofushi, Tokyo 182, Japan.  Department of Computer Science, State University of New York at Buffalo, 226...
Inverting Onto Functions
, 1996
"... We look at the hypothesis that all honest onto polynomialtime computable functions have a polynomialtime computable inverse. We show this hypothesis equivalent to several other complexity conjectures including ffl In polynomial time, one can find accepting paths of nondeterministic polynomialtim ..."
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Cited by 37 (6 self)
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We look at the hypothesis that all honest onto polynomialtime computable functions have a polynomialtime computable inverse. We show this hypothesis equivalent to several other complexity conjectures including ffl In polynomial time, one can find accepting paths of nondeterministic polynomialtime Turing machines that accept \Sigma . ffl Every total multivalued nondeterministic function has a polynomialtime computable refinement. ffl In polynomial time, one can compute satisfying assignments for any polynomialtime computable set of satisfiable formulae. ffl In polynomial time, one can convert the accepting computations of any nondeterministic Turing machine that accepts SAT to satisfying assignments. We compare these hypotheses with several other important complexity statements. We also examine the complexity of these statements where we only require a single bit instead of the entire inverse. 1 Introduction Understanding the power of nondeterminism has been one of the pri...
Counting Beyond a Yottabyte, or how SPARQL 1.1 Property Paths will Prevent Adoption of the Standard
"... SPARQL –the standard query language for querying RDF – provides only limited navigational functionalities, although these features are of fundamental importance for graph data formats such as RDF. This has led the W3C to include the property path feature in the upcoming version of the standard, SPAR ..."
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Cited by 26 (2 self)
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SPARQL –the standard query language for querying RDF – provides only limited navigational functionalities, although these features are of fundamental importance for graph data formats such as RDF. This has led the W3C to include the property path feature in the upcoming version of the standard, SPARQL 1.1. We tested several implementations of SPARQL 1.1 handling property path queries, and we observed that their evaluation methods for this class of queries have a poor performance even in some very simple scenarios. To formally explain this fact, we conduct a theoretical study of the computational complexity of property paths evaluation. Our results imply that the poor performance of the tested implementations is not a problem of these particular systems, but of the specification itself. In fact, we show that any implementation that adheres to the SPARQL 1.1 specification (as of November 2011) is doomed to show the same behavior, the key issue being the need for counting solutions imposed by the current specification. We provide several intractability results, that together with our empirical results, provide strong evidence against the current semantics of SPARQL 1.1 property paths. Finally, we put our results in perspective, and propose a natural alternative semantics with tractable evaluation, that we think may lead to a wide adoption of the language by practitioners, developers and theoreticians.
Probabilistic Logic under Coherence: Complexity and Algorithms
 In Proceedings ISIPTA01
, 2001
"... We study probabilistic logic under the viewpoint of the coherence principle of de Finetti. In detail, we explore the relationship between coherencebased and classical modeltheoretic probabilistic logic. Interestingly, we show that the notions of gcoherence and of gcoherent entailment can be expre ..."
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Cited by 25 (12 self)
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We study probabilistic logic under the viewpoint of the coherence principle of de Finetti. In detail, we explore the relationship between coherencebased and classical modeltheoretic probabilistic logic. Interestingly, we show that the notions of gcoherence and of gcoherent entailment can be expressed by combining notions in modeltheoretic probabilistic logic with concepts from default reasoning. Using these results, we analyze the computational complexity of probabilistic reasoning under coherence. Moreover, we present new algorithms for deciding gcoherence and for computing tight gcoherent intervals, which reduce these tasks to standard reasoning tasks in modeltheoretic probabilistic logic. Thus, efficient techniques for modeltheoretic probabilistic reasoning can immediately be applied for probabilistic reasoning under coherence, for example, column generation techniques. We then describe two other interesting techniques for efficient modeltheoretic probabilistic reasoning in the conjunctive case.
Predicatecalculus based logics for modeling and solving search problems
 ACM Transactions on Computational Logic
, 2006
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Competing Provers Yield Improved KarpLipton Collapse Results
 Information and Computation
, 2002
"... Via competing provers, we show that if a language A is selfreducible and has polynomialsize circuits then S 2 = S 2 . Building on this, we strengthen the Kamper AFK Theorem, namely, we prove that if NP coNP)/poly then the polynomial hierarchy collapses to S 2 . We also strengthen Yap ..."
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Cited by 23 (3 self)
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Via competing provers, we show that if a language A is selfreducible and has polynomialsize circuits then S 2 = S 2 . Building on this, we strengthen the Kamper AFK Theorem, namely, we prove that if NP coNP)/poly then the polynomial hierarchy collapses to S 2 . We also strengthen Yap's Theorem, namely, we prove that if NP coNP/poly then the polynomial hierarchy collapses to S 2 . Under the same assumptions, the best previously known collapses were to ZPP respectively ([KW98, BCK 94], building on [KL80, AFK89, Kam91, Yap83]). It is known that S 2 [Cai01]. That result and its relativized version show that our new collapses indeed improve the previously known results. Since the Kamper AFK Theorem and Yap's Theorem are used in the literature as bridges in a variety of resultsranging from the study of unique solutions to issues of approximationour results implicitly strengthen all those results.
Disjoint NPPairs
, 2003
"... We study the question of whether the class DisNP of disjoint pairs (A, B) of NPsets contains a complete pair. The question relates to the question of whether optimal proof systems exist, and we relate it to the previously studied question of whether there exists a disjoint pair of NPsets that is N ..."
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Cited by 22 (8 self)
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We study the question of whether the class DisNP of disjoint pairs (A, B) of NPsets contains a complete pair. The question relates to the question of whether optimal proof systems exist, and we relate it to the previously studied question of whether there exists a disjoint pair of NPsets that is NPhard. We show under reasonable hypotheses that nonsymmetric disjoint NPpairs exist, which provides additional evidence for the existence of Pinseparable disjoint NPpairs. We construct
On The Computational Complexity of Inferring Evolutionary Trees
, 1993
"... The process of reconstructing evolutionary trees can be viewed formally as an optimization problem. Recently, decision problems associated with the most commonly used approaches to reconstructing such trees have been shown to be NPcomplete [Day87, DJS86, DS86, DS87, GF82, Kri88, KM86]. In this t ..."
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Cited by 20 (5 self)
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The process of reconstructing evolutionary trees can be viewed formally as an optimization problem. Recently, decision problems associated with the most commonly used approaches to reconstructing such trees have been shown to be NPcomplete [Day87, DJS86, DS86, DS87, GF82, Kri88, KM86]. In this thesis, a framework is established that incorporates all such problems studied to date. Within this framework, the NPcompleteness results for decision problems are extended by applying theorems from [CT91, Gas86, GKR92, JVV86, KST89, Kre88, Sel91] to derive bounds on the computational complexity of several functions associated with each of these problems, namely ffl evaluation functions, which return the cost of the optimal tree(s), ffl solution functions, which return an optimal tree, ffl spanning functions, which return the number of optimal trees, ffl enumeration functions, which systematically enumerate all optimal trees, and ffl randomselection functions, which return a random...