A Quantitative Study of Pure Parallel Processes
Abstract
In this paper, we study the interleaving  or pure merge  operator that most often characterizes parallelism in concurrency theory. This operator is a principal cause of the socalled combinatorial explosion that makes very hard  at least from the point of view of computational complexity  the analysis of process behaviours e.g. by modelchecking. The originality of our approach is to study this combinatorial explosion phenomenon on average, relying on advanced analytic combinatorics techniques. We study various measures that contribute to a better understanding of the process behaviours represented as plane rooted trees: the number of runs (corresponding to the width of the trees), the expected total size of the trees as well as their overall shape. Two practical outcomes of our quantitative study are also presented: (1) a lineartime algorithm to compute the probability of a concurrent run prefix, and (2) an efficient algorithm for uniform random sampling of concurrent runs. These provide interesting responses to the combinatorial explosion problem.
 Publication:

arXiv eprints
 Pub Date:
 July 2014
 arXiv:
 arXiv:1407.1873
 Bibcode:
 2014arXiv1407.1873B
 Keywords:

 Computer Science  Programming Languages
 EPrint:
 Electronic Journal of Combinatorics, 23, 1, (2016), P1.11