Community-based 3-SAT formulas with a predefined solution

It is crucial to generate SAT formulas with predefined solutions for the development of SAT solvers since many SAT formulas from real-world applications have solutions. Although some algorithms have been proposed to generate SAT formulas with predefined solutions, community structures of SAT formulas are not considered in these algorithms. Consequently, we propose a 3-SAT formula generating algorithm that not only guarantees the existence of a predefined solution, but also simultaneously considers community structures and clause distributions. To study the effect of community structures and clause distributions on the hardness of SAT formulas, we measure solving runtimes of two solvers, gluHack and CPSparrow, on the generated SAT formulas under different parameter settings. Through extensive experiments, we obtain some noteworthy observations. For example, the community structure has few or no effects on the hardness of SAT formulas with regard to CPSparrow but a strong effect with regard to gluHack. Copyright © 2021 Inderscience Enterprises Ltd.