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447
The PL Hierarchy Collapses
, 1995
"... It is shown that the PL hierarchy PLH = PL S PL PL S PL PL PL S \Delta \Delta \Delta, defined in terms of the RuzzoSimonTompa relativization, collapses to PL. Also, it is shown that PL is closed under logspaceuniform AC 0 reductions. 1 Introduction The power of probabilistic computati ..."
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Cited by 13 (2 self)
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It is shown that the PL hierarchy PLH = PL S PL PL S PL PL PL S \Delta \Delta \Delta, defined in terms of the RuzzoSimonTompa relativization, collapses to PL. Also, it is shown that PL is closed under logspaceuniform AC 0 reductions. 1 Introduction The power of probabilistic
The Log Space Oracle Hierarchy Collapses
, 1987
"... this paper we show that the log space oracle hierarchy also collapses, that it thus does coincide with the log space alternation hierarchy, and that the resulting complexity class L has other interesting characterizations in terms of circuits with oracle gates ..."
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Cited by 1 (1 self)
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this paper we show that the log space oracle hierarchy also collapses, that it thus does coincide with the log space alternation hierarchy, and that the resulting complexity class L has other interesting characterizations in terms of circuits with oracle gates
SynthesisGuided Partial Hierarchy Collapsing
"... This paper presents a framework for analyzing distribution of sequentially equivalent nodes in a hierarchical design. This information can be used for selectively collapsing hierarchical modules into 'supermodules ' resulting in improved optimization and better placement decisions. Our fr ..."
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This paper presents a framework for analyzing distribution of sequentially equivalent nodes in a hierarchical design. This information can be used for selectively collapsing hierarchical modules into 'supermodules ' resulting in improved optimization and better placement decisions. Our
Does the Polynomial Hierarchy Collapse if Onto Functions are Invertible?
"... Abstract. The class TFNP, defined by Megiddo and Papadimitriou, consists of multivalued functions with values that are polynomially verifiable and guaranteed to exist. Do we have evidence that such functions are hard, for example, if TFNP is computable in polynomialtime does this imply the polynomi ..."
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the polynomialtime hierarchy collapses? By computing a multivalued function in deterministic polynomialtime we mean on every input producing one of the possible values of the function on that input. We give a relativized negative answer to this question by exhibiting an oracle under which TFNP functions
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
Graph Nonisomorphism Has Subexponential Size Proofs Unless The PolynomialTime Hierarchy Collapses
 SIAM Journal on Computing
, 1998
"... We establish hardness versus randomness tradeoffs for a broad class of randomized procedures. In particular, we create efficient nondeterministic simulations of bounded round ArthurMerlin games using a language in exponential time that cannot be decided by polynomial size oracle circuits with acce ..."
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Cited by 110 (4 self)
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with access to satisfiability. We show that every language with a bounded round ArthurMerlin game has subexponential size membership proofs for infinitely many input lengths unless exponential time coincides with the third level of the polynomialtime hierarchy (and hence the polynomialtime hierarchy
The µCalculus Alternation Hierarchy Collapses over Structures with Restricted Connectivity
"... It is known that the alternation hierarchy of least and greatest fixpoint operators in the µcalculus is strict. However, the strictness of the alternation hierarchy does not necessarily carry over when considering restricted classes of structures. A prominent instance is the class of infinite word ..."
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It is known that the alternation hierarchy of least and greatest fixpoint operators in the µcalculus is strict. However, the strictness of the alternation hierarchy does not necessarily carry over when considering restricted classes of structures. A prominent instance is the class of infinite
The µCalculus Alternation Hierarchy Collapses over Structures with Restricted Connectivity
"... It is known that the alternation hierarchy of least and greatest fixpoint operators in the µcalculus is strict. However, the strictness of the alternation hierarchy does not necessarily carry over when considering restricted classes of structures. A prominent instance is the class of infinite word ..."
Abstract
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It is known that the alternation hierarchy of least and greatest fixpoint operators in the µcalculus is strict. However, the strictness of the alternation hierarchy does not necessarily carry over when considering restricted classes of structures. A prominent instance is the class of infinite
What’s up with downward collapse: Using the easyhard technique to link boolean and polynomial hierarchy collapses
 DEPARTMENT OF COMPUTER SCIENCE, UNIVERSITY OF ROCHESTER
, 1998
"... During the past decade, nine papers have obtained increasingly strong consequences from the assumption that boolean or boundedquery hierarchies collapse. The final four papers of this ninepaper progression actually achieve downward collapse—that is, they show that highlevel collapses induce col ..."
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Cited by 13 (7 self)
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During the past decade, nine papers have obtained increasingly strong consequences from the assumption that boolean or boundedquery hierarchies collapse. The final four papers of this ninepaper progression actually achieve downward collapse—that is, they show that highlevel collapses induce
Trading Group Theory for Randomness
, 1985
"... In a previous paper [BS] we proved, using the elements of the Clwory of nilyotenf yroupu, that some of the /undamcnla1 computational problems in mat & proup, belong to NP. These problems were also ahown to belong to CONP, assuming an unproven hypofhedi.9 concerning finilc simple Q ’ oup,. The a ..."
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Cited by 353 (9 self)
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prove th:rt. in spite of their analogy with the polynomial time hierarchy, the finite levrls of this hierarchy collapse t,o Afsf=Ah42). Using a combinatorial lemma on finite groups [IIE], we construct a game by whirh t.he nondeterministic player (Merlin) is able to coavlnre the random player (Arthur
Results 1  10
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447