Abstract
We study the following problems on some classes of randomly generated logic programs under the answer set semantics: the existence of an answer set and the hardness of finding one answer set, if any.
Firstly in logic programs with 3 or more literals in the rules, for the first problem, despite the non-monotonicity of the answer set semantics, we observe a phase transition occurring on some particular critical values of L/N, where L and N are the number of rules and atoms in a program, respectively. More specifically, the probability of having an answer set drops from near 1 to near 0 abruptly and monotonically when the ratio increases from 0 to ∞. For the second problem, we find that for all three of the systems that we have tested: Smodels, DLV, and ASSAT, the problem of finding one answer set becomes much harder when the ratio falls into a certain region. Our experiments also show that a logic program without answer sets is much harder to compute than those with. This suggests that the most effective strategies for improving the performance of ASP systems should be those that can detect the non-existence of answer sets early on. In a class of logic program with 2 or 3 literals in the rules, we observe an interesting non-monotonicity on the probability of existing answer sets, which coincides with the non-monotonicity of the answer set semantics.
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Zhao, Y., Lin, F. (2003). Answer Set Programming Phase Transition: A Study on Randomly Generated Programs. In: Palamidessi, C. (eds) Logic Programming. ICLP 2003. Lecture Notes in Computer Science, vol 2916. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24599-5_17
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DOI: https://doi.org/10.1007/978-3-540-24599-5_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20642-2
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