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Abstract. We compare the expressive power of process calculi by studying the problem of electing a leader in a symmetric network of processes. We consider the π-calculus with mixed choice and with separate choice, value-passing CCS and Mobile Ambients. We provide a unified approach for all these calculi using reduction semantics. 1

We investigate classes of systems based on different interaction patterns with the aim of achieving distributability. As our system model we use Petri nets. In Petri nets, an inherent concept of simultaneity is built in, since when a transition has more than one preplace, it can be crucial that tokens are removed instantaneously. When modelling a system which is intended to be implemented in a distributed way by a Petri net, this built-in concept of synchronous interaction may be problematic. To investigate the problem we assume that removing tokens from places can no longer be considered as instantaneous. We model this by inserting silent (unobservable) transitions between transitions and their preplaces. We investigate three different patterns for modelling this type of asynchronous interaction. Full asynchrony assumes that every removal of a token from a place is time consuming. For symmetric asynchrony, tokens are only removed slowly in case of backward branched transitions, hence where the concept of simultaneous removal actually occurs. Finally we consider a more intricate pattern by allowing to remove tokens from preplaces of backward branched transitions asynchronously in sequence (asymmetric asynchrony). We investigate the effect of these different transformations of instantaneous interaction into asynchronous interaction patterns by comparing the behaviours of nets before and after insertion of the silent transitions. We exhibit for which classes of Petri nets we obtain equivalent behaviour with respect to failures equivalence. It turns out that the resulting hierarchy of Petri net classes can be described by semi-structural properties. In case of full asynchrony and symmetric asynchrony, we obtain precise characterisations; for asymmetric asynchrony we obtain lower and upper bounds. We briefly comment on possible applications of our results to Message Sequence Charts.

Abstract. When considering distributed systems, it is a central issue how to deal with interactions between components. In this paper, we investigate the paradigms of synchronous and asynchronous interaction in the context of distributed systems. We investigate to what extent or under which conditions synchronous interaction is a valid concept for specification and implementation of such systems. We choose Petri nets as our system model and consider different notions of distribution by associating locations to elements of nets. First, we investigate the concept of simultaneity which is inherent in the semantics of Petri nets when transitions have multiple input places. We assume that tokens may only be taken instantaneously by transitions on the same location. We exhibit a hierarchy of ‘asynchronous ’ Petri net classes by different assumptions on possible distributions. Alternatively, we assume that the synchronisations specified in a Petri net are crucial system properties. Hence transitions and their preplaces may no longer placed on separate locations. We then answer the question which systems may be implemented in a distributed way without restricting concurrency, assuming that locations are inherently sequential. It turns out that in both settings we find semi-structural properties of Petri nets describing exactly the problematic situations for interactions in distributed systems. 1

the asynchronous nature of the asynchronous

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Abstract. We address the question of what kind of asynchronous communication is exactly modeled by the asynchronous π-calculus (πa). To this purpose we define a calculus πB where channels are represented explicitly as special buffer processes. The base language for πB is the (synchronous) π-calculus, except that ordinary processes communicate only via buffers. Then we compare this calculus with πa. It turns out that there is a strong correspondence between πa and πB in the case that buffers are bags: we can indeed encode each πa process into a strongly asynchronous bisimilar πB process, and each πB process into a weakly asynchronous bisimilar πa process. In case the buffers are queues or stacks, on the contrary, the correspondence does not hold. We show indeed that it is not possible to translate a stack or a queue into a weakly asynchronous bisimilar πa process. Actually, for stacks we show an even stronger result, namely that they cannot be encoded into weakly (asynchronous) bisimilar processes in a π-calculus without mixed choice. 1