The Combinatorics of Non-determinism

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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Conference papers
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https://hal.archives-ouvertes.fr/hal-01216553
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Submitted on : Friday, October 16, 2015 - 2:31:57 PM
Last modification on : Thursday, March 21, 2019 - 2:30:50 PM

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Olivier Bodini, Antoine Genitrini, Frédéric Peschanski. The Combinatorics of Non-determinism. IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, Dec 2013, Guwahati, India. pp.425-436, ⟨10.4230/LIPIcs.FSTTCS.2013.425⟩. ⟨hal-01216553⟩

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