A Collaborative Framework for Non-Linear Integer Arithmetic Reasoning in Alt-Ergo

Sylvain Conchon 1, 2 Mohamed Iguernelala 3 Alain Mebsout 1, 2
1 TOCCATA - Certified Programs, Certified Tools, Certified Floating-Point Computations
LRI - Laboratoire de Recherche en Informatique, UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR8623
Abstract : In this paper, we describe a collaborative framework for reasoning modulo simple properties of non-linear integer arithmetic. This framework relies on the AC(X) combination method and on interval calculus. The first component is used to handle equalities of linear integer arithmetic and associativity and commutativity properties of non-linear multiplication. The interval calculus component is used - in addition to standard linear operations over inequalities - to refine bounds of non-linear terms and to inform the SAT solver about judicious case-splits on bounded intervals. The framework has been implemented in the Alt-Ergo theorem prover. We show its effectiveness on a set of formulas generated from deductive program verification.
Type de document :
Pré-publication, Document de travail
2013
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Contributeur : Sylvain Conchon <>
Soumis le : mardi 7 janvier 2014 - 10:21:22
Dernière modification le : jeudi 9 février 2017 - 15:58:04
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Sylvain Conchon, Mohamed Iguernelala, Alain Mebsout. A Collaborative Framework for Non-Linear Integer Arithmetic Reasoning in Alt-Ergo. 2013. <hal-00924646>

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