Abstract. We study causality in the ß-calculus. Our notion of causality combines the dependencies given by the syntactic structure of processes with those originated by passing names. It turns out that two transitions not causally related may although occur in a fixed ordering in any computation, i.e., ß-calculus may express implicitly a priority between actions. Our causality relation still induces the same partial order of transitions for all the computations that are obtained by shuffling transitions that are concurrent (= related neither by causality nor by priority). The presentation takes advantage from a parametric definition of process behaviour that highlights the essence of the topic. All the results on bisimulation based equivalences, congruences, axiomatizations and logics are taken (almost) for free from the interleaving theory. 1 Introduction The study of the behaviour of a distributed system may benefit from knowledge on the causal relation between its events. For examp...

We propose an event based semantics for contextual nets, i.e. an extension of Place/Transition Petri nets where transitions can also have context conditions, modelling resources that can be read without being consumed. The result is a generalization of Winskel’s work on safe nets: the event based semantics is given at categorical level via a chain of coreflections leading from the category WS-CN of weakly safe contextual nets to the category Dom of finitary prime algebraic domains. A fundamental rôle is played by the notion of asymmetric event structures that generalize Winskel’s prime event structures, following an idea similar to that of “possible flow ” introduced by Pinna and Poignè. Asymmetric event structures have the usual causal relation of traditional prime event structures, but replace the symmetric conflict with a relation modelling asymmetric conflict or weak causality. Such relation allows one to represent the new kind of dependency between events arising in contextual nets, as well as the usual symmetric conflict. Moreover it is used in a non-trivial way in the definition of the ordering of configurations, which is different from the standard set-inclusion.

We present an event structure semantics for contextual nets, an extension of P/T Petri nets where transitions can check for the presence of tokens without consuming them (read-only operations). A basic rôle is played by asymmetric event structures, a generalization of Winskel’s prime event structures where symmetric conflict is replaced by a relation modelling asymmetric conflict or weak causality, used to represent a new kind of dependency between events arising in contextual nets. Extending Winskel’s seminal work on safe nets, the truly concurrent event based semantics of contextual nets is given at categorical level via a chain of coreflections

Models for concurrency can be classified with respect to three relevant parameters: behaviour/system, interleaving/noninterleaving, linear/branching time. When modelling a process, a choice concerning such parameters corresponds to choosing the level of abstraction of the resulting semantics. In this paper, we move a step towards a classification of models for concurrency based on the parameters above. Formally, we choose a representative of any of the eight classes of models obtained by varying the three parameters, and we study the formal relationships between using the language of category theory.

We describe a new `real-time' process algebra with simple semantics but considerable expressivepower. It exhibits the advantages of both the `constraint-oriented' and `marker variable' specification styles. The definition extends Milner's CCS, firstly with a simple notion of absolute time added to actions, and then with relative timing expressions which may refer to time markers.

CHIARA BODEI Dipartimento di Informatica, Universit`a di Pisa Corso Italia, 40, I-56125 Pisa, Italy chiara@di.unipi.it The paper defines a taxonomy of concurrent models. Concurrent models are seen as categories and passages between models as functors. We particularly care about the notions of concurrency, causal and temporal dependencies and their possible different perception. According to the chosen model, only part of these notions are, indeed, relevant and recoverable from the observation of a concurrent system. 1 Introduction In the last decades a great deal of efforts have been devoted to study suitable models in order to describe concurrent and distributed systems and to understand their semantics. Several and heterogeneous models have been introduced, each focusing on a peculiar aspect of concurrency and laying at a particular description level. Categories, as in 1;2;3 , can help in classifying the different models and in formally characterizing the passages between them. ...

We relate sheaf and trace models of concurrency for an interacting community of objects with a discrete linear infinitary model of time. The sheaf model can be more easily generalized for other assumptions about time, and has broader connections to other models of concurrency. The traces model is more accessible, and is probably sufficient for modelling synchronous concurrency in practical object-oriented languages.

The specification, verification, design and implementation of real-time system is a major software engineering problem. While logical correctness is a major issue in the development of large and complex software systems, real-time system development demands that timing correctness be satisfied additionally. Formal methods of specification and verification are imperative for this task, and there has been considerable research in the area for the past two decades. Of these, state-transition based techniques are numerous and well-developed. This paper attempts to compare the approaches taken by workers in the area and provide an introduction to the major issues facing a real-time system developer who wishes to use one of these formal methods.