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arXiv · 1907.04243

The Combinatorics of Barrier Synchronization

Olivier Bodini·Matthieu Dien·Antoine Genitrini·Frédéric Peschanski
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Abstract

In this paper we study the notion of synchronization from the point of view of combinatorics. As a first step, we address the quantitative problem of counting the number of executions of simple processes interacting with synchronization barriers. We elaborate a systematic decomposition of processes that produces a symbolic integral formula to solve the problem. Based on this procedure, we develop a generic algorithm to generate process executions uniformly at random. For some interesting sub-classes of processes we propose very efficient counting and random sampling algorithms. All these algorithms have one important characteristic in common: they work on the control graph of processes and thus do not require the explicit construction of the state-space.

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Olivier Bodini, Matthieu Dien, Antoine Genitrini, Frédéric Peschanski. 2019-07-03. The Combinatorics of Barrier Synchronization. https://doi.org/10.1007/978-3-030-21571-2_21

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