Open Bisimulation for the Concurrent Constraint Pi-Calculus

The concurrent constraint pi-calculus (cc-pi-calculus) has been introduced as a model for concluding Service Level Agreements. The cc-pi calculus combines the synchronous communication paradigm of process calculi with the constraint handling mechanism of concurrent constraint programming. While in the original presentation of the calculus a reduction semantics has been proposed, in this work we investigate the abstract semantics of cc-pi processes. First, we define a labelled transition system of the calculus and a notion of open bisimilarity à la pi-calculus that is proved to be a congruence. Next, we give a symbolic characterisation of bisimulation and we prove that the two semantics coincide. Essentially, two processes are open bisimilar if they have the same stores of constraints this can be statically checked and if their moves can be mutually simulated. A key idea of the symbolic transition system is to have ‘contextual’ labels, i.e. labels specifying that a process can evolve only in presence of certain constraints. Finally, we show that the polyadic Explicit Fusions calculus introduced by Gardner and Wischik can be translated into monadic cc-pi and that such a transition preserves open bisimilarity. The mapping exploits fusions and tuple unifications as constraints.