Random k-GD-SAT model and its phase transition

Abstract

We present a new type of SAT problem called the k-GD-SAT, which generalizes k-SAT and GD-SAT. In k-GD-SAT, clause lengths have geometric distribution, controlled by a probability parameter p; for p = 1, a k-GD-SAT problem is a k-SAT problem. We report on the phase transition between satisfiability and unsatisfiability for randomly generated instances of k-GD-SAT. We provide theoretical analysis and experimental results suggesting that there is an intriguing relationship (linear in the parameter 1/p) between crossover points for different parameters of k-GD-SAT. We also consider a relationship between crossover points for k-SAT and k-GD-SAT and provide links between these values. © J.UCS.