Pseudo-Industrial Random SAT Generators

Recent advances in SAT are focused on efficiently solving real-world or industrial problems. However, the reduced number of industrial SAT instances and the high cost of solving them condition the development and debugging processes of new techniques. This problem can be solved by defining new models of random SAT instance that capture realistically the main features of the real-world SAT instances. In this work, we review some of these models, and we define a new model in which we are working on. The Classical Random model [8] was popularized to study the SAT/UNSAT phase transition phenomena, and the easy-hard-easy associated pattern, both dependent on the clause/variable ratio. In this model, k-CNF formulas consist of m independent clauses among the 2k ( n k ) clauses with k literals on n variables that are neither simplifiable nor tautologies. This model does not capture the main features of real-world problems, and SAT solvers perform very differently on random and industrial SAT instances. One important feature of industrial SAT instance is the scale-free structure [2]. This means that the number of variables occurrences follows, in general, a power-law distribution p(k) ∝ k−α, and these distributions are scale-free. This implies that there exists a big variability in the number of occurrences of variables. This kind of structure is very characteristic in real-world networks. Preferential Attachment [6] was proposed as a model to explain this behavior in growing networks. Scale-free random SAT formulas [3] were proposed as an alternative model that also reproduce this feature. This model is parametric in the exponent α, and generates formulas as set of independent clauses, where the clause with variables {i1, . . . , ik} ⊆ {1, . . . , n} has probability P (i1 ∨ . . . ∨ ik) ∼ ∏k j=1(ij) 1 α−1 . Another important feature shared by the majority of industrial benchmarks is the community structure (or high modularity) [4, 5], meaning that they are characterized by a partition of communities of highly connected variables, i.e., they usually appear in clauses with variables of the same community. The Community Attachment model [7] was proposed to generate instances with this structure. It is parametric on a modularity Q and number of communities c. Formulas are also sets of independent clauses, where, with probability Q+ 1/c, all their literals belong to the same community; otherwise, all of them belong to distinct communities. This generates formulas with modularity at least Q.