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546
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 Ruzzo-Simon-Tompa relativization, collapses to PL. Also, it is shown that PL is closed under logspace-uniform 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 Ruzzo-Simon-Tompa relativization, collapses to PL. Also, it is shown that PL is closed under logspace-uniform AC 0 -reductions. 1 Introduction The power of probabilistic
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 /undamcn-la1 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 lev-rls of this hierarchy collapse t,o Afsf=Ah42). Using a com-binatorial lemma on finite groups [IIE], we construct a game by whirh t.he nondeterministic player (Merlin) is able to coavlnre the random player (Arthur
Relational Queries Computable in Polynomial Time
- Information and Control
, 1986
"... We characterize the polynomial time computable queries as those expressible in relational calculus plus a least fixed point operator and a total ordering on the universe. We also show that even without the ordering one application of fixed point suffices to express any query expressible with several ..."
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Cited by 318 (17 self)
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with several alternations of fixed point and negation. This proves that the fixed point query hierarchy suggested by Chandra and Harel collapses at the first fixed point level. It is also a general result showing that in finite model theory one application of fixed point suffices. Introduction and Summary
View-dependent simplification of arbitrary polygonal environments
, 1997
"... Hierarchical dynamic simplification (HDS) is a new approach to the problem of simplifying arbitrary polygonal environments. HDS operates dynamically, retessellating the scene continuously as the user’s viewing position shifts, and adaptively, processing the entire database without first decomposing ..."
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Cited by 286 (15 self)
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viewdependent simplification. Briefly, HDS works by clustering vertices together in a hierarchical fashion. The simplification process continuously queries this hierarchy to generate a scene containing only those polygons that are important from the current viewpoint. When the volume of space associated with a
Nondeterministic Space is Closed Under Complementation
, 1988
"... this paper we show that nondeterministic space s(n) is closed under complementation, for s(n) greater than or equal to log n. It immediately follows that the context-sensitive languages are closed under complementation, thus settling a question raised by Kuroda in 1964 [9]. See Hartmanis and Hunt [4 ..."
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Cited by 262 (14 self)
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on the collapse of the log space hierarchies [10, 2, 14]. We have shown that the class (FO + pos TC) is closed under complementation. Our
Graph Nonisomorphism Has Subexponential Size Proofs Unless The Polynomial-Time Hierarchy Collapses
- SIAM Journal on Computing
, 1998
"... We establish hardness versus randomness trade-offs for a broad class of randomized procedures. In particular, we create efficient nondeterministic simulations of bounded round Arthur-Merlin 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 Arthur-Merlin game has subexponential size membership proofs for infinitely many input lengths unless exponential time coincides with the third level of the polynomial-time hierarchy (and hence the polynomial-time hierarchy
Use of Hierarchy in Fault Collapsing
"... We discuss the advantage of using hierarchy in testing. Our demonstration is based on the problem of fault collapsing. Though this problem is not considered to be too complex, the time of collapsing faults in moderately large circuits can be several hours or more. This can be considerably shortened ..."
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We discuss the advantage of using hierarchy in testing. Our demonstration is based on the problem of fault collapsing. Though this problem is not considered to be too complex, the time of collapsing faults in moderately large circuits can be several hours or more. This can be considerably shortened
The Collapse of the Bounded Width Hierarchy
, 2014
"... We show that every constraint satisfaction problem over a fixed constraint language that has bounded relational width has also relational width (2, 3). Together with known results this gives a trichotomy for width: a constraint satisfaction problem has either relational width 1, or relational width ..."
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Cited by 1 (0 self)
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We show that every constraint satisfaction problem over a fixed constraint language that has bounded relational width has also relational width (2, 3). Together with known results this gives a trichotomy for width: a constraint satisfaction problem has either relational width 1, or relational width (2, 3) (and no smaller width), or does not have bounded relational width.
Computing Solutions Uniquely Collapses the Polynomial Hierarchy
- SIAM Journal on Computing
, 1993
"... Is there a single-valued 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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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 single-valued NP refinement," our result provides the strongest evidence yet that multivalued NP
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
Results 1 - 10
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546