On the Structure of Industrial SAT Instances
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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- [ABL09]Ansótegui, C., Bonet, M.L., Levy, J.: Towards industrial-like random SAT instances. In: Proc. of the 21st Int. Joint Conf. on Artificial Intelligence, IJCAI 2009 (2009)Google Scholar
- [CSN07]Clauset, A., Shalizi, C.R., Newman, M.E.J.: Power-law distributions in empirical data. Arxiv, 0706.1062 (2007)Google Scholar
- [GHPW99]Gent, I.P., Hoos, H.H., Prosser, P., Walsh, T.: Morphing: Combining structure and randomness. In: Proc. of the 16th Nat. Conf. on Artificial Intelligence, AAAI 1999, pp. 654–660 (1999)Google Scholar
- [LA97]Li, C.M., Anbulagan: Look-ahead versus look-back for satisfiability problems. In: Smolka, G. (ed.) CP 1997. LNCS, vol. 1330, pp. 341–355. Springer, Heidelberg (1997)Google Scholar
- [Sel00]Selman, B.: Satisfiability testing: Recent developments and challenge problems. In: Proc. of the 15th Annual IEEE Symposium on Logic in Computer Science, LICS 2000, p. 178 (2000)Google Scholar
- [SKM97]Selman, B., Kautz, H.A., McAllester, D.A.: Ten challenges in propositional reasoning and search. In: Proc. of the 15th Int. Joint Conf. on Artificial Intelligence, IJCAI 1997, pp. 50–54 (1997)Google Scholar
- [Wal01]Walsh, T.: Search on high degree graphs. In: Proc. of the 17th Int. Joint Conf. on Artificial Intelligence, IJCAI 2001, pp. 266–274 (2001)Google Scholar