Scale-Free Random SAT Instances
Carlos Ansótegui, Marı́a Luisa Bonet, Jordi Levy · Algorithms · 2022
We focus on the random generation of SAT instances that have properties similar to real-world instances. It is known that many industrial instances, even with a great number of variables, can be solved by a clever solver in a reasonable amount of time. This is not possible, in general, with classical randomly generated instances. We provide a different generation model of SAT instances, called scale-free random SAT instances. This is based on the use of a non-uniform probability distribution P(i)∼i−β to select variable i, where β is a parameter of the model. This results in formulas where the number of occurrences k of variables follows a power-law distribution P(k)∼k−δ, where δ=1+1/β. This property has been observed in most real-world SAT instances. For β=0, our model extends classical random SAT instances. We prove the existence of a SAT–UNSAT phase transition phenomenon for scale-free random 2-SAT instances with β1−1/k, the unsatisfiability of most formulas may be due to small cores of clauses. Finally, we show how this model will allow us to generate random instances similar to industrial instances, of interest for testing purposes.