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Precise Widening Operators for Convex Polyhedra

Roberto Bagnara
Dipartimento di Matematica
Università di Parma
Via M. D'Azeglio 85/A
I-43100 Parma
Italy

Katy Dobson
School of Computing
University of Leeds
Leeds, LS2 9JT
United Kingdom

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

Matthew Mundell
School of Computing
University of Leeds
Leeds, LS2 9JT
United Kingdom

Enea Zaffanella
Dipartimento di Matematica
Università di Parma
Via M. D'Azeglio 85/A
I-43100 Parma
Italy

Abstract

This paper explores the abstract domain of grids, a domain that is able to represent sets of equally spaced points and hyperplanes over an n-dimensional vector space. Such a domain is useful for the static analysis of the patterns of distribution of the values program variables can take. Besides the bare abstract domain, we present a complete set of operations on grids that includes all that is necessary to define the abstract semantics and the widening operators required to compute it in a finite number of steps. The definition of the domain and its operations exploit well-known techniques from linear algebra as well as a dual representation that allows, among other things, for a concise and efficient implementation.

Available: Gzipped postscript, BibTeX entry.

[Page last updated on 2005/12/22.]