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Abstract: Contrary to the sequential world, the processes involved in a distributedsystem do not necessarily know when a computation is globally finished. Thispaper investigates the problem of the detection of the termination of localcomputations. We define four types of termination detection: no detection,detection of the local termination, detection by a distributed observer,detection of the global termination. We give a complete characterisationexcept in the local termination detection case where a partial one is givenfor each of this termination detection and show that they define a stricthierarchy. These results emphasise the difference between computability of adistributed task and termination detection. Furthermore, thesecharacterisations encompass all standard criteria that are usually formulated :topological restriction tree, rings, or triangu- lated networks

.,topological knowledge size, diameter

., and local knowledge to distinguishnodes identities, sense of direction. These results are now presented ascorollaries of generalising theorems. As a very special and important case, thetechniques are also applied to the election problem. Though given in the modelof local computations, these results can give qualitative insight for similarresults in other standard models. The necessary conditions involve graphscovering and quasi-covering; the sufficient conditions constructive localcomputations are based upon an enumeration algorithm of Mazurkiewicz and astable properties detection algorithm of Szymanski, Shi and Prywes.

Autor: Emmanuel Godard LIF, Yves Métivier LaBRI, Gerard Tel

Fuente: https://arxiv.org/

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