Satisfiability Modulo Transcendental Functions via Incremental Linearization

Alessandro Cimatti; Alberto Griggio; Ahmed Irfan; Marco Roveri; Roberto Sebastiani

doi:10.1007/978-3-319-63046-5_7

International Conference on Automated Deduction

CADE 2017: Automated Deduction – CADE 26 pp 95-113

Satisfiability Modulo Transcendental Functions via Incremental Linearization

Authors
Authors and affiliations

Alessandro Cimatti
Alberto Griggio
Ahmed IrfanEmail author
Marco Roveri
Roberto Sebastiani

Conference paper

First Online:: 11 July 2017

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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Authors and Affiliations

Alessandro Cimatti
- 1
Alberto Griggio
- 1
Ahmed Irfan
- 1
- 2
Email author
Marco Roveri
- 1
Roberto Sebastiani
- 2

1.Fondazione Bruno KesslerTrentoItaly
2.DISI, University of TrentoTrentoItaly

About this paper

Cite this paper as:: Cimatti A., Griggio A., Irfan A., Roveri M., Sebastiani R. (2017) Satisfiability Modulo Transcendental Functions via Incremental Linearization. In: de Moura L. (eds) Automated Deduction – CADE 26. CADE 2017. Lecture Notes in Computer Science, vol 10395. Springer, Cham

DOI https://doi.org/10.1007/978-3-319-63046-5_7
Publisher Name Springer, Cham
Print ISBN 978-3-319-63045-8
Online ISBN 978-3-319-63046-5
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Satisfiability Modulo Transcendental Functions via Incremental Linearization

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