文章基本信息

标题：Graph Width Measures for CNF-Encodings with Auxiliary Variables
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作者：Stefan Mengel ; Romain Wallon
期刊名称：Journal of Artificial Intelligence Research
印刷版ISSN：1076-9757
出版年度：2020
卷号：67
页码：409-436
出版社：American Association of Artificial
摘要：We consider bounded width CNF-formulas where the width is measured by popular graph width measures on graphs associated to CNF-formulas. Such restricted graph classes, in particular those of bounded treewidth, have been extensively studied for their uses in the design of algorithms for various computational problems on CNF-formulas. Here we consider the expressivity of these formulas in the model of clausal encodings with auxiliary variables. We first show that bounding the width for many of the measures from the literature leads to a dramatic loss of expressivity, restricting the formulas to those of low communication complexity. We then show that the width of optimal encodings with respect to different measures is strongly linked: there are two classes of width measures, one containing primal treewidth and the other incidence cliquewidth, such that in each class the width of optimal encodings only differs by constant factors. Moreover, between the two classes the width differs at most by a factor logarithmic in the number of variables. Both these results are in stark contrast to the setting without auxiliary variables where all width measures we consider here differ by more than constant factors and in many cases even by linear factors.
关键词：knowledge representation;mathematical foundations;satisfiability