Boosting Local Consistency Algorithms over Floating-Point Numbers

  • Mohammed Said Belaid
  • Claude Michel
  • Michel Rueher
Conference paper

DOI: 10.1007/978-3-642-33558-7_12

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7514)
Cite this paper as:
Belaid M.S., Michel C., Rueher M. (2012) Boosting Local Consistency Algorithms over Floating-Point Numbers. In: Milano M. (eds) Principles and Practice of Constraint Programming. Lecture Notes in Computer Science, vol 7514. Springer, Berlin, Heidelberg

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 \(\mathcal{F}\).

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Copyright information

© 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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