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

Olivier Bodini | Zendy; Matthieu Dien | Zendy; Antoine Genitrini | Zendy; Frédéric Peschanski | Zendy

Open Access

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

Author(s) -

Olivier Bodini,

Matthieu Dien,

Antoine Genitrini,

Frédéric Peschanski

Publication year - 2017

Language(s) - English

Resource type - Conference proceedings

DOI - 10.1137/1.9781611974775.2

Subject(s) - colored , closure (psychology) , fork (system call) , product (mathematics) , class (philosophy) , mathematics , interpretation (philosophy) , set (abstract data type) , discrete mathematics , extension (predicate logic) , computer science , combinatorics , materials science , geometry , artificial intelligence , economics , market economy , composite material , programming language , operating system

International audienceIn 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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