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Widening operators for powerset domains

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A Publisher's Erratum to this article was published on 27 February 2007

Abstract

The finite powerset construction upgrades an abstract domain by allowing for the representation of finite disjunctions of its elements. While most of the operations on the finite powerset abstract domain are easily obtained by “lifting” the corresponding operations on the base-level domain, the problem of endowing finite powersets with a provably correct widening operator is still open. In this paper we define three generic widening methodologies for the finite powerset abstract domain. The widenings are obtained by lifting any widening operator defined on the base-level abstract domain and are parametric with respect to the specification of a few additional operators that allow all the flexibility required to tune the complexity/precision trade-off. As far as we know, this is the first time that the problem of deriving non-trivial, provably correct widening operators in a domain refinement is tackled successfully. We illustrate the proposed techniques by instantiating our widening methodologies on powersets of convex polyhedra, a domain for which no non-trivial widening operator was previously known.

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Authors and Affiliations

  1. Department of Mathematics, University of Parma, Italy

    Roberto Bagnara & Enea Zaffanella

  2. School of Computing, University of Leeds, UK

    Patricia M. Hill

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  1. Roberto Bagnara
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  2. Patricia M. Hill
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  3. Enea Zaffanella
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Correspondence to Roberto Bagnara.

Additional information

An erratum to this article is available at http://dx.doi.org/10.1007/s10009-007-0029-y.

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Bagnara, R., Hill, P.M. & Zaffanella, E. Widening operators for powerset domains. Int J Softw Tools Technol Transfer 8, 449–466 (2006). https://doi.org/10.1007/s10009-005-0215-8

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