Abstract
This paper presents a CNF SAT-formulae transformation technique employing Gröbner bases as a means to analyze the problem structure. Gröbner-bases have been applied in the past for SAT; however, their use was primarily restricted to analyzing entire problems for proof-refutation. In contrast, this technique analyzes limited subsets of problems, and uses the derived Gröbner bases to yield new constraint-information. This information is then used to reduce problem structure, provide additional information about the problem itself, or aid other preprocessing techniques. Contrary to the precepts of contemporary techniques, the transformation often increases the problem size. However, experimental results demonstrate that our approach often improves SAT-search efficiency in a number of areas, including: solve time, conflicts, number of decisions, etc.
This work is supported, in part, by a Faculty Early Career Development (CAREER) grant from the US National Science Foundation, contract No. CCF-546859.
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Condrat, C., Kalla, P. (2007). A Gröbner Basis Approach to CNF-Formulae Preprocessing. In: Grumberg, O., Huth, M. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2007. Lecture Notes in Computer Science, vol 4424. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71209-1_48
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