Linear Integer Arithmetic Revisited

  • Martin BrombergerEmail author
  • Thomas Sturm
  • Christoph Weidenbach
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9195)


We consider feasibility of linear integer programs in the context of verification systems such as SMT solvers or theorem provers. Although satisfiability of linear integer programs is decidable, many state-of-the-art solvers neglect termination in favor of efficiency. It is challenging to design a solver that is both terminating and practically efficient. Recent work by Jovanović and de Moura constitutes an important step into this direction. Their algorithm CUTSAT is sound, but does not terminate, in general. In this paper we extend their CUTSAT algorithm by refined inference rules, a new type of conflicting core, and a dedicated rule application strategy. This leads to our algorithm CUTSAT++, which guarantees termination.


Linear arithmetic SMT SAT DPLL Linear programming Integer arithmetic 



This research was supported in part by the German Transregional Collaborative Research Center SFB/TR 14 AVACS and by the ANR/DFG project STU 483/2-1 SMArT.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Martin Bromberger
    • 1
    Email author
  • Thomas Sturm
    • 1
  • Christoph Weidenbach
    • 1
  1. 1.Max Planck Institute for InformaticsSaarbrückenGermany

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