The Combinatorics of Barrier Synchronization
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.
Cite
@article{arxiv.1907.04243,
title = {The Combinatorics of Barrier Synchronization},
author = {Olivier Bodini and Matthieu Dien and Antoine Genitrini and Frédéric Peschanski},
journal= {arXiv preprint arXiv:1907.04243},
year = {2019}
}