On Using Floating-Point Computations to Help an Exact Linear Arithmetic Decision Procedure [chapter]

David Monniaux
2009 Lecture Notes in Computer Science  
We consider the decision problem for quantifier-free formulas whose atoms are linear inequalities interpreted over the reals or rationals. This problem may be decided using satisfiability modulo theory (SMT), using a mixture of a SAT solver and a simplex-based decision procedure for conjunctions. State-of-the-art SMT solvers use simplex implementations over rational numbers, which perform well for typical problems arising from model-checking and program analysis (sparse inequalities, small
more » ... icients) but are slow for other applications (denser problems, larger coefficients). We propose a simple preprocessing phase that can be adapted to existing SMT solvers and that may be optionally triggered. Despite using floating-point computations, our method is sound and completeit merely affects efficiency. We implemented the method and provide benchmarks showing that this change brings a naive and slow decision procedure ("textbook simplex" with rational numbers) up to the efficiency of recent SMT solvers, over test cases arising from model-checking, and makes it definitely faster than state-of-the-art SMT solvers on dense examples. This work was partially funded by the ANR ARPEGE project "ASOPT". VERIMAG is a joint laboratory of CNRS, Université Joseph Fourier and Grenoble-INP.
doi:10.1007/978-3-642-02658-4_42 fatcat:f5um44i5qja4hpwkwhpqjwk2ge