Further Results on Partial Order Equivalences on Infinite Systems

In [26], we investigated decidability issues for standard language equivalence for process description languages with two generalisations based on traditional approaches<br />for capturing non-interleaving behaviour: pomset equivalence reflecting global causal dependency, and location equivalence reflecting spatial distribution of events. In this paper, we continue by investigating the role played by TCSP-style renaming and hiding combinators with respect to decidability. One result of [26] was that in contrast to pomset equivalence, location equivalence remained decidable for a class of processes consisting of finite sets of BPP processes communicating in a TCSP manner. Here, we show that location equivalence becomes undecidable when either renaming or hiding is added to this class of processes. Furthermore, we investigate the weak versions of location and pomset equivalences.<br />We show that for BPP with prefixing, both weak pomset and weak location equivalence are decidable. Moreover, we show that weak location equivalence is undecidable for BPP semantically extended with CCS communication.

OBSERVING DISTRIBUTION IN PROCESSES: STATIC AND DYNAMIC LOCALITIES

The distributed structure of CCS processes can be made explicit by assigning different locations to their parallel components. These locations then become part of what is observed of a process. The assignment of locations may be done statically, or dynamically as the execution proceeds. The dynamic approach was developed first, in Refs. [4,5], as it appeared to be more convenient for defining notions of location equivalence and preorder. Extending previous work by L. Aceto1 we study here the static approach, which is more natural from an intuitive point of view, and more manageable for verification purposes. We define static notions of location equivalence and preorder, and show that they coincide with the dynamic ones. To establish the equivalence of the two location semantics, we introduce an intermediate transition system called occurrence system, which incorporates both notions of locality. This system supports a definition of local history preserving bisimulation for CCS, which is a third formulation of location equivalence.