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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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https://hal.sorbonne-universite.fr/hal-01448695
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Submitted on : Thursday, February 2, 2017 - 3:32:16 PM
Last modification on : Saturday, February 15, 2020 - 1:51:01 AM
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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. pp.16 - 30, ⟨10.1137/1.9781611974775.2⟩. ⟨hal-01448695⟩

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