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.

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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.

In this paper we discuss the issue of interleaving semantics versus True concurrency in an algebraic setting. We present various equivalence notions on Petri nets which can be used in the construction of algebraic models: (a) the occurrence net equivalence of Nielsen, Plotkin & Winskel; (b) bisimulation equivalence, which leads to a model which is isomorphic to the graph model of Baeten, Bergstra & Klop; (c) the concurrent bisimulation equivalence, which is also described by Nielsen & Thiagarajan, and Goltz; (d) partial order equivalences which are inspired by work of Pratt, and Boadol & CastellanL A central role in the paper will be played by the notion of reat4ime consistency. We show that, besides occurrence net equivalence, none of the equivalences mentioned above (including the partial order equivaJer~ces!) is reaI-time consistent. Therefore we introduce the notion of S~-bisimutation equivalence, which is real-time consistent. Moreover a complete proo! system will be presented for those finite ST-bisimutation processes in which no action can occur concurrently with itself. Note: Partial support received from the European Communities under ESPRIT project no. 432, An integrated Formal Approach to Industrial Software Development (METEOR). INTRODUCTIONOne of the most controversial issues in the theory of concurrency is the issue of interleaving semantics versus True concurrency. People advocating interleaving semantics model the parallel composition of two processes by interleaving the atomic actions performed by these processes. A typical equation valid in interleaving semantics is: a lib = a.b +b.a. The intended meaifing of this equation is that when you observe the parallel composition of atomic actions a and b, either you see first the a and then the b, or you see first the b and then the a. The interleaving fans are aware of the fact that for some applications their approach is not realistic (for example in those places where realtime or fairness aspects are important). But since reality is extremely complicated one needs some simplifying assumptions, and they argue that the interleaving assumption is a good one: it allows for the construction of very elegant mathematical models of concurrency in which specification and verification of large concurrent systems is feasible.The True concurrency adherents on the contrary think that interleaving models are very unrealistic. With an enormous enthusiasm they present all kinds of examples, formulated in terms of Petri nets, event structures or Mazurkiewicz traces, which show that the interleaving approach is bizarre.Another controversy in the theory of concurrency which we would like to mention here is the issue of linear time versus branching time. It has to do with the equation: a'(b +c) = a.b+a.c. Here the intended meaning is that when you observe first a and then b or c, this is just the same as when you observe a and then b or a and then c. Most True concurrency theories use this equation because the people who developed these theories thought there was nothi...

This paper explores the connection between semantic equivalences and preorders for concrete sequential processes, represented by means of labeled transition systems, and formats of transition system specifications using Plotkin's structural approach. For several preorders in the linear timebranching time spectrum a format is given, as general as possible, such that this preorder is a precongruence for all operators specifiable in that format. The formats are derived using the modal characterizations of the corresponding preorders.

A cornerstone of the theory of proof nets for unit-free multiplicative linear logic (MLL) is the abstract representation of cut-free proofs modulo inessential commutations of rules. The only known extension to additives, based on monomial weights, fails to preserve this key feature: a host of cut-free monomial proof nets can correspond to the same cut-free proof. Thus the problem of finding a satisfactory notion of proof net for unit-free multiplicativeadditive linear logic (MALL) has remained open since the inception of linear logic in 1986. We present a new definition of MALL proof net which remains faithful to the cornerstone of the MLL theory.

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