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On look-ahead heuristics in disjunctive logic programming

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Abstract

Disjunctive logic programming (DLP), also called answer set programming (ASP), is a convenient programming paradigm which allows for solving problems in a simple and highly declarative way. The language of DLP is very expressive and able to represent even problems of high complexity (every problem in the complexity class \({{\Sigma}_{2}^{P}} = {\rm NP}^{{\rm NP}}\)). During the last decade, efficient systems supporting DLP have become available. Virtually all of these systems internally rely on variants of the Davis–Putnam procedure (for deciding propositional satisfiability [SAT]), combined with a suitable model checker. The heuristic for the selection of the branching literal (i.e., the criterion determining the literal to be assumed true at a given stage of the computation) dramatically affects the performance of a DLP system. While heuristics for SAT have received a fair deal of research, only little work on heuristics for DLP has been done so far. In this paper, we design, implement, optimize, and experiment with a number of heuristics for DLP. We focus on different look-ahead heuristics, also called “dynamic heuristics” (the DLP equivalent of unit propagation [UP] heuristics for SAT). These are branching rules where the heuristic value of a literal Q depends on the result of taking Q true and computing its consequences. We motivate and formally define a number of look-ahead heuristics for DLP programs. Furthermore, since look-ahead heuristics are computationally expensive, we design two techniques for optimizing the burden of their computation. We implement all the proposed heuristics and optimization techniques in DLV—the state-of-the-art implementation of disjunctive logic programming, and we carry out experiments, thoroughly comparing the heuristics and optimization techniques on a large number of instances of well-known benchmark problems. The results of these experiments are very interesting, showing that the proposed techniques significantly improve the performance of the DLV system.

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Authors and Affiliations

  1. Department of Mathematics, University of Calabria, 87036, Rende (CS), Italy

    Wolfgang Faber, Nicola Leone, Gerald Pfeifer & Francesco Ricca

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  1. Wolfgang Faber
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  2. Nicola Leone
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  3. Gerald Pfeifer
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  4. Francesco Ricca
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Corresponding author

Correspondence to Nicola Leone.

Additional information

Some results in this paper have been presented in preliminary form at IJCAI-01 [16], LPNMR’01 [17], and LPNMR’05 [18].

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Faber, W., Leone, N., Pfeifer, G. et al. On look-ahead heuristics in disjunctive logic programming. Ann Math Artif Intell 51, 229–266 (2007). https://doi.org/10.1007/s10472-008-9087-4

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