Re nement and State Machine

Most SVRC technical reports are available via anonymous ftp, from svrc.it.uq.edu.au in the directory /pub/techreports. Abstracts and compressed postscript les are available via Abstract Precise module interface speciications are essential in modular software development. The role of state in these speciications has been the issue of some debate and is central to the notion of data reenement. In previous work, Hooman and Strooper introduce a state-abstraction lattice that deenes a partial order on speciications for deterministic and complete languages. They use this lattice to deene a notion of state abstractness and show that this intuitive notion corresponds to the use of the terms \abstract" and \concrete" as used in data-reenement proofs. In this paper, we extend this work for a class of speciications and languages that we call demonic and semi-deterministic. We also introduce a notion of backward reenement and prove that backward reenement together with the common forward reenement of VDM and Z form a sound and complete reenement technique with respect to a partial order on languages deened by demonic speciications. We illustrate the ideas using simple languages and speciications.