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2009
Springer

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

9 years 12 months ago
On Using Floating-Point Computations to Help an Exact Linear Arithmetic Decision Procedure
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 eff...
David Monniaux
Added 12 Aug 2010
Updated 12 Aug 2010
Type Conference
Year 2009
Where CAV
Authors David Monniaux
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