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    GRASP: A New Search Algorithm for Satisfiability

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    This paper introduces GRASP (Generic search Algorithm J3r the Satisfiabilily Problem), an integrated algorithmic J3amework 30r SAT that unifies several previously proposed searchpruning techniques and jcilitates identification of additional ones. GRASP is premised on the inevitability of conflicts during search and its most distinguishingjature is the augmentation of basic backtracking search with a powerful conflict analysis procedure. Analyzing conflicts to determine their causes enables GRASP to backtrack non-chronologically to earlier levels in the search tree, potentially pruning large portions of the search space. In addition, by 'ecording" the causes of conflicts, GRASP can recognize and preempt the occurrence of similar conflicts later on in the search. Einally, straighrward bookkeeping of the causali y chains leading up to conflicts a/lows GRASP to identij) assignments that are necessary jr a solution to be found. Experimental results obtained jom a large number of benchmarks, including many J3om the field of test pattern generation, indicate that application of the proposed conflict analysis techniques to SAT algorithms can be extremely ejctive jr a large number of representative classes of SAT instances

    Adoption of simultaneous different strategies against different opponents enhances cooperation

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    The emergence of cooperation has been widely studied in the context of game theory on structured populations. Usually the individuals adopt one strategy against all their neighbors. The structure can provide reproductive success for the cooperative strategy, at least for low values of defection tendency. Other mechanisms, such punishment, can also be responsible for cooperation emergence. But what happens if the players adopt simultaneously different strategies against each one of their opponents, not just a single one? Here we study this question in the prisoner dilemma scenario structured on a square lattice and on a ring. We show that if an update rule is defined in which the players replace the strategy that furnishes the smallest payoff, a punishment response mechanism against defectors without imputing cost to the punishers appears, cooperation dominates and, even if the tendency of defection is huge, cooperation still remains alive
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