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A New Method for 3-Satisfiability Problem Phase Transition on Structural Entropy

The phenomenon of phase transition is an important property of the satisfiability (SAT) problem. It not only determines the difficulty of solving the problem, but also plays an important role in designing fast solving algorithms. The structural entropy is an effective method to measure the complexity of graph structure. It maps the proposition formula to the graph structure, and then gives the structural entropy of it. A new method of 3-SAT phase transition measurement based on structural entropy is proposed. Through numerical experiments on the random 3-SAT instance set, the results show that the satisfiability of the random 3-SAT problem has phase transition with the change of structural entropy. At the same time, it is very difficult to solve the problem in the region near the phase transition point.