For a smooth integration of classical automata theory and concurrency theory, one would like to consider process algebras including a constant denoting successful termination and binary operations for alternative and sequential composition. Using alternative composition and successful termination it is possible to express a notion of intermediate acceptance as it occurs, e.g., in (classical) finite automata. Sequential composition is necessary for the process-theoretic counterpart of context-free grammars. A process algebra including said ingredients with their traditional semantics, however, also inherits the less desirable phenomenon of transparency: behaviour of the first component of a sequential composition may be skipped.
We present a revised semantics for sequential composition that retains the properties needed for a smooth integration of classical automata theory and concurrency theory, but eliminates transparency. For the resulting process algebra we have obtained axiomatisation and decidability results.
(based on joint work with Jos Baeten, Astrid Belder and Fei Yang)