An Extended Expansion Theorem

Closed CCS (CCCS) is a CCS-like algebra of processes with a generalized form of prefixing based on a full-fledged algebra of transitions rather than on basic actions only. The basic idea is that the generalized prefixing operator takes a transition t, or rather its observation ω, a process E and yields the process t.E. From an operational standpoint, the process t.E may evolve to E by performing a transition labelled by ω. By exploiting the algebra of transitions, we define a general form of expansion theorem which is the heart of a finite axiomatization of a strong observational equivalence for finite CCCS agents. By adding the axioms concerning the interpretation of the operations of the algebra of observations, we still obtain a sound and complete axiomatization of the corresponding bisimulation equivalence. For instance, it is possible to define the classical expansion theorem, or versions of it which handle partial ordering based observations.