Advertisement
Published in:
2014 | OriginalPaper | Chapter
The Fractal Dimension of SAT Formulas
Authors : Carlos Ansótegui, Maria Luisa Bonet, Jesús Giráldez-Cru, Jordi Levy
Published in: Automated Reasoning
Publisher: Springer International Publishing
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
Modern 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.