In comparative concurrency semantics, one usually distinguishes between linear time and branching time semantic equivalences. Milner's notion of ohsen~ation equirlalence is often mentioned as the standard example of a branching time equivalence. In this paper we investigate whether observation equivalence really does respect the branching structure of processes, and find that in the presence of the unobservable action 7 of CCS this is not the case.Therefore, the notion of branching hisimulation equivalence is introduced which strongly preserves the branching structure of processes, in the sense that it preserves computations together with the potentials in all intermediate states that are passed through, even if silent moves are involved. On closed KS-terms branching bisimulation congruence can be completely axiomatized by the single axiom scheme: a.(7.(y + z) + y) = a.(y + z)(where a ranges over all actions) and the usual laws for strong congruence.WC also establish that for sequential processes observation equivalence is not preserved under refinement of actions, whereas branching bisimulation is.For a large class of processes, it turns out that branching bisimulation and observation equivalence are the same. As far as we know, all protocols that have been verified in the setting of observation equivalence happen to fit in this class, and hence are also valid in the stronger setting of branching hisimulation equivalence.

No abstract

No abstract

In this paper I compare the expressive power of several models of concurrency based on their ability to represent causal dependence. To this end, I translate these models, in behaviour preserving ways, into the model of higher dimensional automata, which is the most expressive model under investigation. In particular, I propose four different translations of Petri nets, corresponding to the four different computational interpretations of nets found in the literature. I also extend various equivalence relations for concurrent systems to higher dimensional automata. These include the history preserving bisimulation, which is the coarsest equivalence that fully respects branching time, causality and their interplay, as well as the ST-bisimulation, a branching time respecting equivalence that takes causality into account to the extent that it is expressible by actions overlapping in time. Through their embeddings in higher dimensional automata, it is now well-defined whether members of different models of concurrency are equivalent.