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Satisfiability Allows No Nontrivial Sparsification Unless The PolynomialTime Hierarchy Collapses
 ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY, REPORT NO. 38 (2010)
, 2010
"... Consider the following twoplayer communication process to decide a language L: The first player holds the entire input x but is polynomially bounded; the second player is computationally unbounded but does not know any part of x; their goal is to cooperatively decide whether x belongs to L at small ..."
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Cited by 56 (2 self)
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that the polynomialtime hierarchy collapses to its third level. The result even holds when the first player is conondeterministic, and is tight as there exists a trivial protocol for ǫ = 0. Under the hypothesis that coNP is not in NP/poly, our result implies tight lower bounds for parameters of interest in several
On the hardness of satisfiability with bounded occurrences in the polynomialtime hierarchy
 Theory of Computing
"... Abstract: In 1991, Papadimitriou and Yannakakis gave a reduction implying the NPhardness of approximating the problem 3SAT with bounded occurrences. Their reduction is based on expander graphs. We present an analogue of this result for the second level of the polynomialtime hierarchy based on supe ..."
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Cited by 2 (1 self)
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Abstract: In 1991, Papadimitriou and Yannakakis gave a reduction implying the NPhardness of approximating the problem 3SAT with bounded occurrences. Their reduction is based on expander graphs. We present an analogue of this result for the second level of the polynomialtime hierarchy based
Polynomialtime multiselectivity
, 1997
"... We introduce a generalization of Selman's Pselectivity that yields a more flexible notion of selectivity, called (polynomialtime) multiselectivity, in which the selector is allowed to operate on multiple input strings. Since our introduction of this class, it has been used [HJRW96] to prove ..."
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Cited by 2 (1 self)
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We introduce a generalization of Selman's Pselectivity that yields a more flexible notion of selectivity, called (polynomialtime) multiselectivity, in which the selector is allowed to operate on multiple input strings. Since our introduction of this class, it has been used [HJRW96
PolynomialTime Hierarchy on Randomized Machines
"... 1 Introduction Proving lower bounds remains one of the most challenging tasks in computationalcomplexity. Satisfiability, the seminal NPcomplete problem, is particularly unyielding in this respect. While we believe that any algorithm for satisfiabilitytakes time linear exponential in the number of ..."
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of variables in the formula, we have been unable to prove superlinear time lower bounds on random access machinesdespite several decades of effort. Additionally, problems complete for higher levels of the polynomialtime hierarchy, while not receiving as much attention, havealso resisted nontrivial time lower
On sparsification for computing treewidth
 In Proceedings of IPEC
, 2013
"... Abstract. We investigate whether an nvertex instance (G, k) of Treewidth, asking whether the graph G has treewidth at most k, can efficiently be made sparse without changing its answer. By giving a special form of orcrosscomposition, we prove that this is unlikely: if there is an > 0 and a p ..."
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Cited by 3 (0 self)
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polynomialtime algorithm that reduces nvertex Treewidth instances to equivalent instances, of an arbitrary problem, with O(n2−) bits, then NP ⊆ coNP/poly and the polynomial hierarchy collapses to its third level. Our sparsification lower bound has implications for structural parameterizations of Treewidth
Polynomialtime computation in matrix groups
, 1999
"... This dissertation investigates deterministic polynomialtime computation in matrix groups over finite fields. Of particular interest are matrixgroup problems that resemble testing graph isomorphism. The main results are instances where the problems admit polynomialtime solutions and methods that e ..."
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Cited by 5 (3 self)
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This dissertation investigates deterministic polynomialtime computation in matrix groups over finite fields. Of particular interest are matrixgroup problems that resemble testing graph isomorphism. The main results are instances where the problems admit polynomialtime solutions and methods
Structure of PolynomialTime Approximation
, 2009
"... Approximation schemes are commonly classified as being either a polynomialtime approximation scheme (ptas) or a fully polynomialtime approximation scheme (fptas). To properly differentiate between approximation schemes for concrete problems, several subclasses have been identified: (optimum)asymp ..."
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the equivalence of eptas to socalled convergent polynomialtime approximation schemes. The results are used to refine the hierarchy of polynomialtime approximation schemes considerably and demonstrate the central position of eptas among approximation schemes. We also present two ways to bridge the hardness gap
On Semantic and TypeTheoretic Aspects of PolynomialTime Computability
, 2001
"... This thesis strives to combine two traditions in theoretical computer science: complexity theory and denotational semantics. The recently proposed setting of game semantics, which provided first syntaxindependent fully abstract models of many programming languages, is used to characterize the polyn ..."
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Cited by 7 (0 self)
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the polynomialtime computable functions as those definable by a certain kind of strategies in twoplayer games. In particular, players must comply with a network protocol that structures the exchange of moves between players and restricts the way games can be modied by them during play. The tight correspondence
AverageCase Complexity Theory and PolynomialTime Reductions
, 2001
"... This thesis studies averagecase complexity theory and polynomialtime reducibilities. The issues in averagecase complexity arise primarily from Cai and Selman's extension of Levin's denition of average polynomial time. We study polynomialtime reductions between distributional problems. ..."
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Cited by 2 (0 self)
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This thesis studies averagecase complexity theory and polynomialtime reducibilities. The issues in averagecase complexity arise primarily from Cai and Selman's extension of Levin's denition of average polynomial time. We study polynomialtime reductions between distributional problems
Results 1  10
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20,247