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Decomposing non-redundant sharing by complementation

Zaffanella, E., Hill, P.M. and Bagnara, R. (2002) Decomposing non-redundant sharing by complementation. Theory and Practice of Logic Programming, 2 (2). pp. 233-261. ISSN 1471-0684

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Abstract

Complementation, the inverse of the reduced product operation, is a technique for systematically finding minimal decompositions of abstract domains. Filé and Ranzato advanced the state of the art by introducing a simple method for computing a complement. As an application, they considered the extraction by complementation of the pair-sharing domain PS from the Jacobs and Langen's set-sharing domain SH. However, since the result of this operation was still SH, they concluded that PS was too abstract for this. Here, we show that the source of this result lies not with PS but with SH and, more precisely, with the redundant information contained in SH with respect to ground-dependencies and pair-sharing.

In fact, a proper decomposition is obtained if the non-redundant version of SH, PSD, is substituted for SH. To establish the results for PSD, we define a general schema for subdomains of SH that includes PSD and Def as special cases. This sheds new light on the structure of PSD and exposes a natural though unexpected connection between Def and PSD. Moreover, we substantiate the claim that complementation alone is not sufficient to obtain truly minimal decompositions of domains. The right solution to this problem is to first remove redundancies by computing the quotient of the domain with respect to the observable behavior, and only then decompose it by complementation.

Item Type: Article
Copyright, Publisher and Additional Information: © 2002 Cambridge University Press
Keywords: Abstract interpretation, domain decomposition, complementation, sharing analysis
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds)
Depositing User: Repository Assistant
Date Deposited: 18 May 2006
Last Modified: 17 Jun 2014 04:00
Published Version: http://journals.cambridge.org/action/displayIssue?...
Status: Published
Publisher: Cambridge University Press
Refereed: Yes
Identification Number: DOI:10.1017/S1471068401001351
URI: http://eprints.whiterose.ac.uk/id/eprint/1205

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