Verifying while loops with invariant relations

Authors:
Asma Louhichi;Wided Ghardallou;Khaled Bsaies;Lamia Labed Jilani;Olfa Mraihi;Ali Mili
Affiliations:
Faculty of Sciences, University of Tunis El Manar, Tunis, 1080, Tunisia;Faculty of Sciences, University of Tunis El Manar, Tunis, 1080, Tunisia;Faculty of Sciences, University of Tunis El Manar, Tunis, 1080, Tunisia;Institut Superieur de Gestion, Bardo 2000, Tunisia;Institut Superieur de Gestion, Bardo 2000, Tunisia;CCS, NJIT, Newark NJ 07102-1982, USA
Venue:
International Journal of Critical Computer-Based Systems
Year:
2014

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Abstract

Traditionally, invariant assertions are used to verify the partial correctness of while loops with respect to pre/post specifications. In this paper we discuss a related but distinct concept, namely invariant relations, and show how invariant relations are a more potent tool in the analysis of while loops: whereas invariant assertions can only be used to prove partial correctness, invariant relations can be used to prove total correctness; also, whereas invariant assertions can only be used to prove correctness, invariant relations can be used to prove correctness and can also be used to prove incorrectness; finally, where traditional studies of loop termination equate termination with iterating a finite number of times, we broaden the definition of termination to also capture the condition that each individual iteration proceeds without raising an exception.