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Title

The Fractal Dimension of SAT Formulas

AuthorsAnsotegui, Carlos; Bonet, Maria Luisa; Giráldez-Crú, Jesús ; Levy, Jordi
KeywordsSAT instances
Fractal dimension
Self-similar
SAT-solving
SAT solvers
Precise definition
Issue Date19-Jul-2014
PublisherSpringer
CitationLecture Notes in Computer Science, vol. 8562. Automated Reasoning, 7th International Joint Conference, IJCAR 2014, Held as Part of the Vienna Summer of Logic, VSL 2014, Vienna, Austria, July 19-22, 2014. Proceedings, pp.107-121
AbstractModern SAT solvers have experienced a remarkable progress on solving industrial instances. Most of the techniques have been developed after an intensive experimental process. It is believed that these techniques exploit the underlying structure of industrial instances. However, there is not a precise definition of the notion of structure. Recently, there have been some attempts to analyze this structure in terms of complex networks, with the long-term aim of explaining the success of SAT solving techniques, and possibly improving them. We study the fractal dimension of SAT instances with the aim of complementing the model that describes the structure of industrial instances. We show that many industrial families of formulas are self-similar, with a small fractal dimension. We also show how this dimension is affected by the addition of learnt clauses during the execution of SAT solvers.
URIhttp://hdl.handle.net/10261/132347
DOIhttp://dx.doi.org/10.1007/978-3-319-08587-6_8
Identifiersdoi: 10.1007/978-3-319-08587-6_8
isbn: 978-331908586-9
Appears in Collections:(IIIA) Comunicaciones congresos
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