The Ordered and Colored Products in Analytic Combinatorics: Application to the Quantitative Study of Synchronizations in Concurrent Processes

Abstract : In this paper, we study two operators for composing combinatorial classes: the ordered product and its dual, the colored product. These operators have a natural interpretation in terms of Analytic Combinatorics, in relation with combinations of Borel and Laplace transforms. Based on these new constructions, we exhibit a set of transfer theorems and closure properties. We also illustrate the use of these operators to specify increasingly labeled structures tightly related to Series-Parallel constructions and concurrent processes. In particular, we provide a quantitative analysis of Fork/Join (FJ) parallel processes, a particularly expressive example of such a class.
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14th Workshop on Analytic Algorithmics and Combinatorics (ANALCO17), Jan 2017, Barcelone, Spain. 2017 Proceedings of the Fourteenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO), pp.16 - 30, 2017, 〈10.1137/1.9781611974775.2〉
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Olivier Bodini, Matthieu Dien, Antoine Genitrini, Frédéric Peschanski. The Ordered and Colored Products in Analytic Combinatorics: Application to the Quantitative Study of Synchronizations in Concurrent Processes. 14th Workshop on Analytic Algorithmics and Combinatorics (ANALCO17), Jan 2017, Barcelone, Spain. 2017 Proceedings of the Fourteenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO), pp.16 - 30, 2017, 〈10.1137/1.9781611974775.2〉. 〈hal-01448695〉

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