A Fast Linear-Arithmetic Solver for DPLL(T)

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Abstract

We present a new Simplex-based linear arithmetic solver that can be integrated efficiently in the DPLL(T) framework. The new solver improves over existing approaches by enabling fast backtracking, supporting a priori simplification to reduce the problem size, and providing an efficient form of theory propagation. We also present a new and simple approach for solving strict inequalities. Experimental results show substantial performance improvements over existing tools that use other Simplex-based solvers in DPLL(T) decision procedures. The new solver is even competitive with state-of-the-art tools specialized for the difference logic fragment.