Quantitative and Algorithmic aspects of Barrier Synchronization in Concurrency

In this paper we address the problem of understanding Concurrency Theory from a combinatorial point of view. We are interested in quantitative results and algorithmic tools to refine our understanding of the classical combinatorial explosion phenomenon arising in concurrency. This paper is essential...

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Bibliographic Details
Published in:Discrete mathematics and theoretical computer science Vol. 22 no. 3, Computational...; no. Special issues
Main Authors: Bodini, OLivier, Dien, Matthieu, Genitrini, Antoine, Peschanski, Frédéric
Format: Journal Article
Language:English
Published: DMTCS 25.01.2021
Discrete Mathematics & Theoretical Computer Science
Series:Computational Logic and Applications (CLA'19)
Subjects:
[info.info-dm]computer science [cs]/discrete mathematics [cs.dm]
[info.info-ds]computer science [cs]/data structures and algorithms [cs.ds]
barrier synchronization
combinatorics
Computer Science
Data Structures and Algorithms
Discrete Mathematics
fork-join processes
partial order theory
promises
uniform random generation
Barrier synchronization
Fork-Join processes
Combinatorics
Uniform random generation
Partial Order Theory
Promises
ISSN:1365-8050, 1462-7264, 1365-8050
Online Access:Get full text
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Summary:In this paper we address the problem of understanding Concurrency Theory from a combinatorial point of view. We are interested in quantitative results and algorithmic tools to refine our understanding of the classical combinatorial explosion phenomenon arising in concurrency. This paper is essentially focusing on the 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.
ISSN:1365-8050
1462-7264
1365-8050
DOI:10.46298/dmtcs.5820