Morphing: combining structure and randomness
AAAI '99/IAAI '99 Proceedings of the sixteenth national conference on Artificial intelligence and the eleventh Innovative applications of artificial intelligence conference innovative applications of artificial intelligence
Satisfiability Testing: Recent Developments and Challenge Problems
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
Regular Random k-SAT: Properties of Balanced Formulas
Journal of Automated Reasoning
Discrete Applied Mathematics
SATzilla: portfolio-based algorithm selection for SAT
Journal of Artificial Intelligence Research
Ten challenges in propositional reasoning and search
IJCAI'97 Proceedings of the 15th international joint conference on Artifical intelligence - Volume 1
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Towards industrial-like random SAT instances
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Empirical study of the anatomy of modern sat solvers
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
Dynamic scoring functions with variable expressions: new SLS methods for solving SAT
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
The community structure of SAT formulas
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
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During this decade, it has been observed that many realworld 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.