Published in

Springer Verlag, Lecture Notes in Computer Science, p. 337-354

DOI: 10.1007/3-540-44898-5_19

Elsevier, Science of Computer Programming, 1-2(58), p. 28-56

DOI: 10.1016/j.scico.2005.02.003



Export citation

Search in Google Scholar

Precise Widening Operators for Convex Polyhedra.

Journal article published in 2003 by Roberto Bagnara, Patricia M. Hill, Elisa Ricci, Enea Zaffanella
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

Full text: Download

Green circle
Preprint: archiving allowed
Green circle
Postprint: archiving allowed
Red circle
Published version: archiving forbidden
Data provided by SHERPA/RoMEO


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 one to gain precision while preserving its overall simplicity.