Harnessing a Refinement Theory to Compute Loop Functions

Authors:
Ali Mili;Rahma Ben Ayed;Shir Aharon;Chaitanya Nadkarni
Affiliations:
College of Computing Science, New Jersey Institute of Technology, Newark NJ 07102, USA;SysCom Ecole Nationale d'Ingénieurs de Tunis, University of Tunis El Manar, Tunis, Tunisia;College of Computing Science, New Jersey Institute of Technology, Newark NJ 07102, USA;College of Computing Science, New Jersey Institute of Technology, Newark NJ 07102, USA
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2009

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Abstract

We consider a while loop on some space S and we are interested in deriving the function that this loop defines between its initial states and its final states (when it terminates). Such a capability is useful in a wide range of applications, including reverse engineering, software maintenance, program comprehension, and program verification. In the absence of a general theoretical solution to the problem of deriving the function of a loop, we explore engineering solutions. In this paper we use a relational refinement calculus to approach this complex problem in a systematic manner. Our approach has many drawbacks, some surmountable and some not (being inherent to the approach); nevertheless, it offers a way to automatically derive the function of loops or an approximation thereof, under some conditions.