Roberto, Margherita and Beatrice

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Precise Widening Operators for Convex Polyhedra

Roberto Bagnara
Dipartimento di Matematica e Informatica
Università di Parma
Parco Area delle Scienze 53/A
I-43124 Parma
Italy

Patricia M. Hill
School of Computing
University of Leeds
Leeds, LS2 9JT
United Kingdom

Elisa Ricci
Dipartimento di Matematica
Università di Parma
Parco Area delle Scienze 53/A
I-43124 Parma
Italy

Enea Zaffanella
Dipartimento di Matematica e Informatica
Università di Parma
Parco Area delle Scienze 53/A
I-43124 Parma
Italy

Abstract

In the context of static analysis via abstract interpretation, convex polyhedra constitute the most used abstract domain among those capturing numerical relational information. Since the domain of convex polyhedra admits infinite ascending chains, it has to be used in conjunction with appropriate mechanisms for enforcing and accelerating the convergence of fixpoint computations. Widening operators provide a simple and general characterization for such mechanisms. For the domain of convex polyhedra, the original widening operator proposed by Cousot and Halbwachs amply deserves the name of standard widening since most analysis and verification tools that employ convex polyhedra also employ that operator. Nonetheless, there is an unfulfilled demand for more precise widening operators. In this paper, after a formal introduction to the standard widening where we clarify some aspects that are often overlooked, we embark on the challenging task of improving on it. We present a framework for the systematic definition of new widening operators that are never less precise than a given widening. The framework is then instantiated on the domain of convex polyhedra so as to obtain a new widening operator that improves on the standard widening by combining several heuristics. A preliminary experimental evaluation has yielded promising results. We also suggest an improvement to the well-known widening delay technique that allows to gain precision while preserving its overall simplicity.


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[Page last updated on January 08, 2005, 21:14:48.]

© Roberto Bagnara
bagnara@cs.unipr.it

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