Solving \(\mathrm {LIA} ^\star \) Using Approximations

  • Maxwell Levatich
  • Nikolaj BjørnerEmail author
  • Ruzica Piskac
  • Sharon Shoham
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11990)


Linear arithmetic with stars, \(\mathrm {LIA} ^\star \), is an extension of Presburger arithmetic that allows forming indefinite summations over values that satisfy a formula. It has found uses in decision procedures for multi-sets and for vector addition systems. \(\mathrm {LIA} ^\star \) formulas can be translated back into Presburger arithmetic, but with non-trivial space overhead. In this paper we develop a decision procedure for \(\mathrm {LIA} ^\star \) that checks satisfiability of \(\mathrm {LIA} ^\star \) formulas. By refining on-demand under and over-approximations of \(\mathrm {LIA} ^\star \) formulas, it can avoid the space overhead that is integral to previous approaches. We have implemented our procedure in a prototype and report on encouraging results that suggest that \(\mathrm {LIA} ^\star \) formulas can be checked for satisfiability without computing a prohibitively large equivalent Presburger formula.


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Maxwell Levatich
    • 1
    • 2
    • 3
  • Nikolaj Bjørner
    • 1
    • 2
    • 3
    Email author
  • Ruzica Piskac
    • 1
    • 2
    • 3
  • Sharon Shoham
    • 1
    • 2
    • 3
  1. 1.YaleNew HavenUSA
  2. 2.Microsoft ResearchRedmondUSA
  3. 3.Tel Aviv UniversityTel AvivIsrael

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