Instantiation of SMT Problems Modulo Integers

  • Mnacho Echenim
  • Nicolas Peltier
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6167)


Many decision procedures for SMT problems rely more or less implicitly on an instantiation of the axioms defining the theories under consideration, and differ by making use of the additional properties of each theory, in order to increase efficiency. We present a new technique for devising complete instantiation schemes on SMT problems over a combination of linear arithmetic with another theory \(\mathcal{T}\). The method consists in first instantiating the arithmetic part of the formula, and then getting rid of the remaining variables in the problem by using an instantiation strategy which is complete for \(\mathcal{T}\). We provide examples evidencing that not only is this technique generic (in the sense that it applies to a wide range of theories) but it is also efficient, even compared to state-of-the-art instantiation schemes for specific theories.


Inequality Variable Decision Procedure Function Symbol Integer Variable Ground Term 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Mnacho Echenim
    • 1
  • Nicolas Peltier
    • 1
  1. 1.University of Grenoble (LIG, Grenoble INP/CNRS) 

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