A Logical Deduction Based Clause Learning Algorithm for Boolean Satisfiability Problems

Clause learning is the key component of modern SAT solvers, while conflict analysis based on the implication graph is the mainstream technology to generate the learnt clauses. Whenever a clause in the clause database is falsified by the current variable assignments, the SAT solver will try to analyze the reason by using different cuts (i.e., the Unique Implication Points) on the implication graph. Those schemes reflect only the conflict on the current search subspace, does not reflect the inherent conflict directly involved in the rest space. In this paper, we propose a new advanced clause learning algorithm based on the conflict analysis and the logical deduction, which reconstructs a linear logical deduction by analyzing the relationship of different decision variables between the backjumping level and the current decision level. The logical deduction result is then added into the clause database as a newly learnt clause. The resulting implementation in Minisat improves the state-of-the-art performance in SAT solving