A fast counterexample minimization approach with refutation analysis and incremental SAT

It is a hotly research topic to eliminate irrelevant variables from counterexample, to make it easier to be understood. BFL algorithm is the most effective counterexample minimization algorithm compared to all other approaches, but its run time overhead is very large due to one call to SAT solver per candidate variable to be eliminated. So we propose a faster counterexample minimization algorithm based on refutation analysis and incremental SAT. First, for every UNSAT instance of BFL, we perform refutation analysis to extract the set of variables that lead to UNSAT, all variables not belong to this set can be eliminated simultaneously. In this way, we can eliminate many variables with only one call to SAT solver. At the same time, we employ incremental SAT approach to share learned clauses between similar instances of BFL, to prevent overlapped state space from being searched repeatedly. Theoretic analysis and experiment result shows that, our approach can be 1 to 2 orders of magnitude faster than BFL, and still retain the minimization ability of BFL (Ravi and Somenzi, 2004).