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Abstract. Traditional incremental SAT solvers have achieved great success in the domain of Bounded Model Checking (BMC). However, modern solvers depend on advanced preprocessing procedures to obtain high levels of performance. Unfortunately, many preprocessing techniques such as a variable and (blocked) clause elimination cannot be directly used in an incremental manner. This work focuses on extending these techniques and Craig interpolation so that they can be used effectively together in incremental SAT solving (in the context of BMC). The techniques introduced here doubled the performance of our BMC solver on both SAT and UNSAT problems. For UNSAT problems, preprocessing had the added advantage that Craig interpolation was able to find the fixed point sooner, reducing the number of incremental SAT iterations. Furthermore, our ideas seem to perform better as the benchmarks become larger, and/or deeper, which is exactly when they are needed. Lastly, our methods can be extended to other SAT based BMC tools to achieve similar speedups.

Abstract. We present a method which computes optimized representations for non-convex polyhedra. Our method detects so-called redundant linear constraints in these representations by using an incremental SMT (Satisfiability Modulo Theories) solver and then removes the redundant constraints based on Craig interpolation. The approach is motivated by applications in the context of model checking for Linear Hybrid Automata. Basically, it can be seen as an optimization method for formulas including arbitrary boolean combinations of linear constraints and boolean variables. We show that our method provides an essential step making quantifier elimination for linear arithmetic much more efficient. Experimental results clearly show the advantages of our approach in comparison to state-of-the-art solvers.

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