Combining CCS and Petri Nets Via Structural Axioms

Many approaches have been developed with the aim of capturing the advantages of both process algebras and Petri nets in terms of modularity and structure on one side and faithful description of concurrency on the other. A natural way of merging these different models is to express the semantics of process algebras in terms of Petri nets. In this work we present a modular construction of operational models for CCS via different groups of structural axioms. To express them, we use Equational Type Logic (ETL), a formalism based on conditional axioms on typed algebras. Typed algebras can be used with profit to present transition systems where both states and transitions have algebraic structure, as opposed to the usual SOS approach where only states have structure. We build an algebra in which different types give different views of the language. In fact, different subalgebras live together in the same structure and are related by axioms. They represent: i) the transition system of CCS; ii) an unfolded version of it; iii) a net for CCS and its marking graph; and iv) a folded version of the latter with the same states as i). The model is completely compositional, since CCS operations are defined on all state representations. We also present axioms which directly establish the relation between interleaving and truly concurrent semantics for CCS. Finally, some related work is discussed and the relation of our models with two previous proposals is shown in detail.