Über Klassen verteilter Petrinetze

This thesis considers -- on a fundamental, and theoretical level -- the question which behaviours respectively algorithms can be realized in a distributed system. It employs Petri nets and various behavioural equivalences to model such systems. Based upon those, it identifies an M-shaped structure as the smallest undistributable Petri net and proves that this identification is stable across a wide swath of the linear-time branching-time spectrum of behavioural equivalences, collected by Glabbeek. It also gives a constructive proof that all Petri nets not containing such a structure are fully distributable. It employs this construction in a prototypical compiler from Petri nets to distributed (via TCP/IP) Linux binaries which was used to test (and fix) said construction. Finally, multiple ways to evade the undistributability theorem's assumptions are discussed, to enable the distributed implementation of necessary behaviours nonetheless.Die Arbeit untersucht -- auf theoretischer und damit fundamentaler Basis -- die Frage welche Verhaltensweisen beziehungsweise Algorithmen durch ein verteiltes System realisiert werden können. Solche Systeme werden dazu durch Petrinetze und verschiedene Verhaltensäquivalenzen modelliert. Innerhalb dieses Modells wird eine M-förmige Struktur als das kleinste unverteilbare Petrinetz identifiziert und gezeigt, dass diese Eigenschaft über einen großen Bereich des durch Glabbeek beschriebenen Linear-Time Branching-Time Spektrums der Verhaltensäquivalenzen stabil bleibt. Die Arbeit enthält weiter einen konstruktiven Beweis, dass alle Petrinetze ohne diese Struktur vollständig verteilbar sind. Die enthaltene Konstruktion wird dann in einem prototypischen Compiler von Petrinetzen nach verteilten (via TCP/IP) Linux-Binaries verwendet, um die Konstruktion zu testen (und zu korrigieren). Schließlich werden verschiedene Wege diskutiert, wie sich die Vorbedingungen des Unverteilbarkeitstheorems umgehen lassen, um notwendige Verhaltensweisen dennoch verteilt implementieren zu können

Synchrony vs. Causality in Asynchronous Petri Nets

Given a synchronous system, we study the question whether the behaviour of that system can be exhibited by a (non-trivially) distributed and hence asynchronous implementation. In this paper we show, by counterexample, that synchronous systems cannot in general be implemented in an asynchronous fashion without either introducing an infinite implementation or changing the causal structure of the system behaviour.Comment: In Proceedings EXPRESS 2011, arXiv:1108.407

Symmetric and Asymmetric Asynchronous Interaction

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 this we consider asynchronous implementations of nets, in which removing tokens from places can no longer be considered as instantaneous. We model this by inserting silent (unobservable) transitions between transitions and some of their preplaces. We investigate three such implementations, differing in the selection of preplaces of a transition from which the removal of a token is considered time consuming, and the possibility of collecting the tokens in a given order. 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. For two of the classes we obtain precise characterisations; for the remaining class we obtain lower and upper bounds. We briefly comment on possible applications of our results to Message Sequence Charts.Comment: 27 pages. An extended abstract of this paper was presented at the first Interaction and Concurrency Experience (ICE'08) on Synchronous and Asynchronous Interactions in Concurrent Distributed Systems, and will appear in Electronic Notes in Theoretical Computer Science, Elsevie

Synchrony versus causality in distributed systems

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.Given a synchronous system, we study the question whether – or, under which conditions – the behaviour of that system can be realized by a (non-trivially) distributed and hence asynchronous implementation. In this paper, we partially answer this question by examining the role of causality for the implementation of synchrony in two fundamental different formalisms of concurrency, Petri nets and the π-calculus. For both formalisms it turns out that each ‘good’ encoding of synchronous interactions using just asynchronous interactions introduces causal dependencies in the translation

On Characterising Distributability

We formalise a general concept of distributed systems as sequential components interacting asynchronously. We define a corresponding class of Petri nets, called LSGA nets, and precisely characterise those system specifications which can be implemented as LSGA nets up to branching ST-bisimilarity with explicit divergence.Comment: arXiv admin note: substantial text overlap with arXiv:1207.359

Synchrony versus causality in distributed systems

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.Given a synchronous system, we study the question whether – or, under which conditions – the behaviour of that system can be realized by a (non-trivially) distributed and hence asynchronous implementation. In this paper, we partially answer this question by examining the role of causality for the implementation of synchrony in two fundamental different formalisms of concurrency, Petri nets and the π-calculus. For both formalisms it turns out that each ‘good’ encoding of synchronous interactions using just asynchronous interactions introduces causal dependencies in the translation