License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2013.425
URN: urn:nbn:de:0030-drops-43901
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2013/4390/
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Bodini, Olivier ; Genitrini, Antoine ; Peschanski, Frédéric

The Combinatorics of Non-determinism

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Abstract

A deep connection exists between the interleaving semantics of concurrent processes and increasingly labelled combinatorial structures. In this paper we further explore this connection by studying the rich combinatorics of partially increasing structures underlying the operator of non-deterministic choice. Following the symbolic method of analytic combinatorics, we study the size of the computation trees induced by typical non-deterministic processes, providing a precise quantitative measure of the so-called "combinatorial explosion" phenomenon. Alternatively, we can see non-deterministic choice as encoding a family of tree-like partial orders. Measuring the (rather large) size of this family on average offers a key witness to the expressiveness of the choice operator. As a practical outcome of our quantitative study, we describe an efficient algorithm for generating computation paths uniformly at random.

BibTeX - Entry

@InProceedings{bodini_et_al:LIPIcs:2013:4390,
  author =	{Olivier Bodini and Antoine Genitrini and Fr{\'e}d{\'e}ric Peschanski},
  title =	{{The Combinatorics of Non-determinism}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)},
  pages =	{425--436},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-64-4},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{24},
  editor =	{Anil Seth and Nisheeth K. Vishnoi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2013/4390},
  URN =		{urn:nbn:de:0030-drops-43901},
  doi =		{10.4230/LIPIcs.FSTTCS.2013.425},
  annote =	{Keywords: Concurrency theory, Analytic combinatorics, Non-deterministic choice, Partially increasing trees, Uniform random generation}
}

Keywords: Concurrency theory, Analytic combinatorics, Non-deterministic choice, Partially increasing trees, Uniform random generation
Collection: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)
Issue Date: 2013
Date of publication: 10.12.2013

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