A Stepwise Development of the Alternating Bit Protocol

In this paper, the theory of fair action systems is used in the specification and development of the Alternating Bit Protocol. A version of the Movers Theorem for fair action systems is proved, which permits the interleaving of actions of one action system within another. This Movers Theorem is applied repeatedly in the development of the Alternating Bit Protocol. 1 Introduction Our aim is to illustrate the usefulness of the theory of fair action systems presented in [Wab96a] through the development of the Alternating Bit Protocol. Particularly by addressing fairness in our approach to the verification of programs, will be able to develop, entirely within the formalism, designs whose infinitary behaviour previously required ad hoc reasoning. The Movers Theorem provides support for introducing concurrency into a development by identifying conditions under which the actions of an iteration executed atomically as a single statement within an action system can be interleaved with their ne..

Developing Fairness in Terminating and Reactive Programs

This paper presents a theory of fairness within the framework of Dijkstra's weakest preconditions and Back's action systems. It is general enough to deal with all kinds of fairness, not just strong and weak fairness. A definition of fairness and refinement to deal with non-terminating programs is also obtained. For terminating and nonterminating programs with and without fairness, theorems about program development such as monotonicity are derived and illustrated by means of examples, principally the readers-writers problem