Satisfiability Modulo Exponential Integer Arithmetic

Lecture notes in computer science, pp. 344–365

Abstract

Abstract SMT solvers use sophisticated techniques for polynomial (linear or non-linear) integer arithmetic. In contrast, non-polynomial integer arithmetic has mostly been neglected so far. However, in the context of program verification, polynomials are often insufficient to capture the behavior of the analyzed system without resorting to approximations. In the last years, incremental linearization has been applied successfully to satisfiability modulo real arithmetic with transcendental functions. We adapt this approach to an extension of polynomial integer arithmetic with exponential functions. Here, the key challenge is to compute suitable lemmas that eliminate the current model from the search space if it violates the semantics of exponentiation. An empirical evaluation of our implementation shows that our approach is highly effective in practice.

Authors 2

1. Florian Frohn Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Aachen, Germany

2. Jürgen Giesl corresponding Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Aachen, Germany