Boosting Local Consistency Algorithms over Floating-Point Numbers

Abstract

Solving constraints over floating-point numbers is a critical issue in numerous applications notably in program verification. Capabilities of filtering algorithms over the floating-point numbers (\(\mathcal{F}\)) have been so far limited to 2b-consistency and its derivatives. Though safe, such filtering techniques suffer from the well known pathological problems of local consistencies, e.g., inability to efficiently handle multiple occurrences of the variables. These limitations also have their origins in the strongly restricted floating-point arithmetic. To circumvent the poor properties of floating-point arithmetic, we propose in this paper a new filtering algorithm, called FPLP, which relies on various relaxations over the real numbers of the problem over \(\mathcal{F}\). Safe bounds of the domains are computed with a mixed integer linear programming solver (MILP) on safe linearizations of these relaxations. Preliminary experiments on a relevant set of benchmarks are promising and show that this approach can be effective for boosting local consistency algorithms over \(\mathcal{F}\).