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PSPACECompleteness of SlidingBlock Puzzles and Other Problems through the Nondeterministic Constraint Logic Model of Computation
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Beyond NP: ArcConsistency for Quantified Constraints
, 2002
"... The generalization of the satisfiability problem with arbitrary quantifiers is a challenging problem of both theoretical and practical relevance. Being PSPACEcomplete, it provides a canonical model for solving other PSPACE tasks which naturally arise in AI. ..."
Abstract

Cited by 46 (5 self)
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The generalization of the satisfiability problem with arbitrary quantifiers is a challenging problem of both theoretical and practical relevance. Being PSPACEcomplete, it provides a canonical model for solving other PSPACE tasks which naturally arise in AI.
Algorithms for quantified constraint satisfaction problems
 In Proceedings of CP2004
, 2004
"... Abstract. Many propagation and search algorithms have been developed for constraint satisfaction problems (CSPs). In a standard CSP all variables are existentially quantified. The CSP formalism can be extended to allow universally quantified variables, in which case the complexity of the basic reaso ..."
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Cited by 22 (2 self)
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Abstract. Many propagation and search algorithms have been developed for constraint satisfaction problems (CSPs). In a standard CSP all variables are existentially quantified. The CSP formalism can be extended to allow universally quantified variables, in which case the complexity of the basic reasoning tasks rises from NPcomplete to PSPACEcomplete. Such problems have, so far, been studied mainly in the context of quantified Boolean formulae. Little work has been done on problems with discrete nonBoolean domains. We attempt to fill this gap by extending propagation and search algorithms from standard CSPs to the quantified case. We also show how the notion of value interchangeability can be exploited to break symmetries and speed up search by orders of magnitude. Finally, we test experimentally the algorithms and methods proposed. 1
full ~playeP 2 ba*,ele~
"... Let PRIVATEPEEK be the resulting game of incomplete information. By requiring that the barriers on the side of player I obscure the locations of all the opponent's plates, we have the blindfold game BLINDPEEK. player: ..."
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Let PRIVATEPEEK be the resulting game of incomplete information. By requiring that the barriers on the side of player I obscure the locations of all the opponent's plates, we have the blindfold game BLINDPEEK. player:
PROBLEM
"... The problem of deciding whether a given propositional formula in conjunctive normal form is satisfiable has been widely studied. It is known that, when restricted to formulas having only two literals per clause, this problem has an efficient (polynomialtime) solution. But the same problem on formul ..."
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The problem of deciding whether a given propositional formula in conjunctive normal form is satisfiable has been widely studied. It is known that, when restricted to formulas having only two literals per clause, this problem has an efficient (polynomialtime) solution. But the same problem on formulas having three literals per clause is NPcomplete, and hence probably does not have any efficient solution. In this paper, we consider an infinite class of satisfiability problems which contains these two particular problems as special cases, and show that every member of this class is either polynomialtime decidable or NPcomplete. The infinite collection of new NPcomplete problems so obtained may prove very useful in finding other new NPcomplete problems. The classification of the polynomialtime decidable cases yields new problems that are complete in polynomial time and in nondeterministic log space. We also consider an analogous class of problems, involving quantified formulas, which has the property that every member is either polynomialtime decidable or complete in polynomial space.