A versatile concept for the analysis of loops

Document Type

Article

Publication Date

7-1-2012

Abstract

Ever since their introduction by Hoare in 1969, invariant assertions have, justifiably, played a key role in the analysis of while loops. In this paper, we discuss a distinct but related concept, viz invariant relations, and show how these can be used to answer many questions pertaining to the analysis of loops, including: how to compute the function of the loop; how to compute an invariant assertion of the loop; how to compute a weakest precondition of the loop; how to compute a strongest postcondition of the loop; how to compute the termination condition of a loop; how to verify whether the loop computes a given function; how to verify whether the loop is correct with respect to a given specification; and finally how to compute an invariant function for the loop. Using a tool we have developed at the University of Tunis to derive invariant relations, we show how all these tasks can be automated by means of a computer algebra system, viz Mathematica (©Wolfram Research). Whenever applicable, we compare the performance of our tool against the performance of others. © 2012 Elsevier Inc. All rights reserved.

Identifier

84861998627 (Scopus)

Publication Title

Journal of Logic and Algebraic Programming

External Full Text Location

https://doi.org/10.1016/j.jlap.2012.04.001

ISSN

15678326

First Page

606

Last Page

622

Issue

5

Volume

81

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