Decidability issues for infinite-state processes- a survey

Over the past decade much attention has been devoted to the study of process calculi such as CCS Mil80, Mil89], ACP BK84, BK88] and CSP Hoa88] as the foundations of a mathematical model for nondeterminism and concurrency. Of particular interest has been the study of the behavioural semantics of these calculi as given by transition graphs arising from structural operational semantics in the tradition originated by Plo81]. In this paper we survey recent developments and current trends within a new eld of study within process algebra, namely that of decidability issues for processes with innnite transition graphs. A particularly important question in process algebra as a whole is when processes can be said to exhibit the same behaviour. As a result, a plethora of behavioural equivalences exist today. The main rationale behind the various behavioural equivalences that have been proposed has been to capture behavioural aspects such as deadlock, livelock and causality that the language equivalence known from language theory does not take into account. For instance, consider the equality ab + ac = a(b + c)