Action systems, unbounded nondeterminism, and infinite traces

Abstract

Abstract Morgan [Mor90a] has described a correspondence between Back's action systems [BKS83] and the conventional failures-divergences model of Hoare's communicating sequential processes (CSP) formalism [Hoa85]. However, the CSP failures-divergences model does not treat unbounded nondeterminism, although unbounded nondeterminism arises quite naturally in action systems; to that extent, the correspondence between the two approaches is inadequate. Fortunately there is an extended infinite traces model of CSP [RoB89] which treats unbounded nondeterminism. We extend the CSP-action system correspondence, using that model instead, to take the unbounded nondeterminism of action systems properly into account. In passing, we develop a definition of the weakest precondition under which an infinite heterogeneous trace of actions is enabled.