On the Structure of Industrial SAT Instances

  • Carlos Ansótegui
  • María Luisa Bonet
  • Jordi Levy
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5732)


During this decade, it has been observed that many real-world graphs, like the web and some social and metabolic networks, have a scale-free structure. These graphs are characterized by a big variability in the arity of nodes, that seems to follow a power-law distribution. This came as a big surprise to researchers steeped in the tradition of classical random networks.

SAT instances can also be seen as (bi-partite) graphs. In this paper we study many families of industrial SAT instances used in SAT competitions, and show that most of them also present this scale-free structure. On the contrary, random SAT instances, viewed as graphs, are closer to the classical random graph model, where arity of nodes follows a Poisson distribution with small variability. This would explain their distinct nature.

We also analyze what happens when we instantiate a fraction of the variables, at random or using some heuristics, and how the scale-free structure is modified by these instantiations. Finally, we study how the structure is modified during the execution of a SAT solver, concluding that the scale-free structure is preserved.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Carlos Ansótegui
    • 1
  • María Luisa Bonet
    • 2
  • Jordi Levy
    • 3
  1. 1.Universitat de Lleida (DIEI, UdL)Spain
  2. 2.Universitat Politècnica de Catalunya (LSI, UPC)Spain
  3. 3.Artificial Intelligence Research Institute (IIIA, CSIC)Spain

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