Action Systems, Unbounded Nondeterminism, and Infinite Traces

Morgan has described a correspondence between Back's action systems and the conventional failures-divergences model of Hoare's communicating sequential processes (CSP) formalism. 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 developed by Roscoe 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