The Combinatorics of Non-determinism

Bodini, Olivier; Genitrini, Antoine; Peschanski, Frédéric

doi:10.4230/LIPIcs.FSTTCS.2013.425

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The Combinatorics of Non-determinism

Authors Olivier Bodini, Antoine Genitrini, Frédéric Peschanski

Part of: Volume: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS)
License: Creative Commons Attribution 3.0 Unported license
Publication Date: 2013-12-10

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Document Identifiers

DOI: 10.4230/LIPIcs.FSTTCS.2013.425
URN: urn:nbn:de:0030-drops-43901

Subject Classification

Keywords

Concurrency theory
Analytic combinatorics
Non-deterministic choice
Partially increasing trees
Uniform random generation

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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.

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Olivier Bodini, Antoine Genitrini, and Frédéric Peschanski. The Combinatorics of Non-determinism. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 24, pp. 425-436, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013) https://doi.org/10.4230/LIPIcs.FSTTCS.2013.425

Author Details

Olivier Bodini

Antoine Genitrini

Frédéric Peschanski

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