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Solving Non-linear Polynomial Arithmetic via SAT Modulo Linear Arithmetic

  • Cristina Borralleras
  • Salvador Lucas
  • Rafael Navarro-Marset
  • Enric Rodríguez-Carbonell
  • Albert Rubio
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5663)

Abstract

Polynomial constraint-solving plays a prominent role in several areas of engineering and software verification. In particular, polynomial constraint solving has a long and successful history in the development of tools for proving termination of programs. Well-known and very efficient techniques, like SAT algorithms and tools, have been recently proposed and used for implementing polynomial constraint solving algorithms through appropriate encodings. However, powerful techniques like the ones provided by the SMT (SAT modulo theories) approach for linear arithmetic constraints (over the rationals) are underexplored to date. In this paper we show that the use of these techniques for developing polynomial constraint solvers outperforms the best existing solvers and provides a new and powerful approach for implementing better and more general solvers for termination provers.

Keywords

Constraint solving polynomial constraints SAT modulo theories termination program analysis 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Cristina Borralleras
    • 1
  • Salvador Lucas
    • 2
  • Rafael Navarro-Marset
    • 2
  • Enric Rodríguez-Carbonell
    • 3
  • Albert Rubio
    • 3
  1. 1.Universidad de VicSpain
  2. 2.Universitat Politècnica de ValènciaSpain
  3. 3.Universitat Politècnica de CatalunyaBarcelonaSpain

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