title = { On using floating-point computations to help an exact linear arithmetic decision procedure },
    author = {Monniaux, David},
    year = {2009},
    booktitle = {Computer-aided verification (CAV)},
    pages = {570--583},
    publisher = {Springer Verlag},
    series = {Lecture Notes in Computer Science},
    volume = {5643},
    team = {SYNC,PACSS},
    pdf = {},
    abstract = {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 coefficients) 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 complete --- it 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. },



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