Conference Paper

Simple Random Logic Programs

DOI: 10.1007/978-3-642-04238-6_20 Conference: Logic Programming and Nonmonotonic Reasoning, 10th International Conference, LPNMR 2009, Potsdam, Germany, September 14-18, 2009. Proceedings
Source: DBLP


We consider random logic programs with two-literal rules and study their properties. In particular, we obtain results on the
probability that random “sparse” and “dense” programs with two-literal rules have answer sets. We study experimentally how
hard it is to compute answer sets of such programs. For programs that are constraint-free and purely negative we show that the easy-hard-easy pattern emerges. We provide arguments to explain that behavior. We also show that the hardness
of programs from the hard region grows quickly with the number of atoms. Our results point to the importance of purely negative
constraint-free programs for the development of ASP solvers.

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    • "In order to apply grammar-based fuzz testing to answer set solvers, methods for generating wide varieties of different answer set programs need to be developed. There are only a few studies that consider the problem of generating random logic programs in the context of ASP (Zhao and Lin 2003; Namasivayam and Truszczy´nski 2009). These studies consider rather restricted subclasses of NLPs and focus on theoretical aspects such as the study of phase transition behavior. "
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    ABSTRACT: This paper develops automated testing and debugging techniques for answer set solver development. We describe a flexible grammar-based black-box ASP fuzz testing tool which is able to reveal various defects such as unsound and incomplete behavior, i.e. invalid answer sets and inability to find existing solutions, in state-of-the-art answer set solver implementations. Moreover, we develop delta debugging techniques for shrinking failure-inducing inputs on which solvers exhibit defective behavior. In particular, we develop a delta debugging algorithm in the context of answer set solving, and evaluate two different elimination strategies for the algorithm. Comment: 18 pages
    Preview · Article · Jul 2010 · Theory and Practice of Logic Programming
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    ABSTRACT: We study simple classes of mixed Horn formulas, in which the structure of the Horn part is drastically constrained. We show that the SAT problem for formulas in these classes remains NP-complete, and demonstrate experimentally that formulas randomly generated from these classes are hard for the present SAT solvers, both complete and local-search ones.
    Preview · Chapter · Jul 2010
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    ABSTRACT: This paper proposes a model, the linear model, for randomly generating logic programs with low density of rules and investigates statistical properties of such random logic programs. It is mathematically shown that the average number of answer sets for a random program converges to a constant when the number of atoms approaches infinity. Several experimental results are also reported, which justify the suitability of the linear model. It is also experimentally shown that, under this model, the size distribution of answer sets for random programs tends to a normal distribution when the number of atoms is sufficiently large.
    Full-text · Article · Jun 2014 · Theory and Practice of Logic Programming