Satisfiability Modulo Transcendental Functions via Incremental Linearization

  • Alessandro Cimatti
  • Alberto Griggio
  • Ahmed Irfan
  • Marco Roveri
  • Roberto Sebastiani
Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10395)

Abstract

In this paper we present an abstraction-refinement approach to Satisfiability Modulo the theory of transcendental functions, such as exponentiation and trigonometric functions. The transcendental functions are represented as uninterpreted in the abstract space, which is described in terms of the combined theory of linear arithmetic on the rationals with uninterpreted functions, and are incrementally axiomatized by means of upper- and lower-bounding piecewise-linear functions. Suitable numerical techniques are used to ensure that the abstractions of the transcendental functions are sound even in presence of irrationals. Our experimental evaluation on benchmarks from verification and mathematics demonstrates the potential of our approach, showing that it compares favorably with delta-satisfiability/interval propagation and methods based on theorem proving.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Alessandro Cimatti
    • 1
  • Alberto Griggio
    • 1
  • Ahmed Irfan
    • 1
    • 2
  • Marco Roveri
    • 1
  • Roberto Sebastiani
    • 2
  1. 1.Fondazione Bruno KesslerTrentoItaly
  2. 2.DISI, University of TrentoTrentoItaly

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