Random k-GD-Sat Model and its Phase Transition

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.