Boosting Local Consistency Algorithms over Floating-Point Numbers

  • Mohammed Said Belaid
  • Claude Michel
  • Michel Rueher
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7514)


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 \(\mathcal{F}\).


Mixed Integer Linear Problem Constraint Programming Multiple Occurrence Vector Encode Safe Bound 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Mohammed Said Belaid
    • 1
  • Claude Michel
    • 1
  • Michel Rueher
    • 1
  1. 1.I3S (UNS/CNRS)Sophia Antipolis CedexFrance

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