@inproceedings{Mon09f,
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 = {http://www-verimag.imag.fr/~monniaux/biblio/Monniaux_CAV09.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. },
}
