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Making abstract models complete

Published online by Cambridge University Press:  12 November 2014

ROBERTO GIACOBAZZI
Affiliation:
Universitá degli Studi di Verona, Dipartimento di Informatica Strada Le Grazie, 15, 37134 Verona, Italy Email: roberto.giacobazzi@univr.it and isabella.mastroeni@univr.it
ISABELLA MASTROENI
Affiliation:
Universitá degli Studi di Verona, Dipartimento di Informatica Strada Le Grazie, 15, 37134 Verona, Italy Email: roberto.giacobazzi@univr.it and isabella.mastroeni@univr.it

Abstract

Completeness is a key feature of abstract interpretation. It corresponds to exactness of the abstraction of fix-points and relies upon the need of absence of false alarms in static program analysis. Making abstract interpretation complete is therefore a major problem in approximating the semantics of programming languages. In this paper, we consider the problem of making abstract interpretations complete by minimally modifying the predicate transformer, i.e. the semantics, of a program. We study the mathematical properties of complete functions on complete lattices and prove the existence of minimal transformations of monotone functions to achieve completeness. We then apply minimal complete transformers to prove the minimality of standard program transformations in security, such as static program monitoring.

Type
Paper
Copyright
Copyright © Cambridge University Press 2014 

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Footnotes

This is a revised and extended version of two papers that appeared in the Proceedings of SAS'08 (Giacobazzi and Mastroeni 2008) and SEFM'08 (Giacobazzi 2008).

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