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The true concurrency of differential interaction nets

Published online by Cambridge University Press:  21 November 2016

DAMIANO MAZZA
DAMIANO MAZZA*
Affiliation:
CNRS, UMR 7030, Laboratoire d'Informatique de Paris Nord, Université Paris 13, Sorbonne Paris Cité, F-93430 Villetaneuse, France Email: [email protected]
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Abstract

We analyse the reduction of differential interaction nets from the point of view of so-called ‘true concurrency,’ that is, employing a non-interleaving model of parallelism. More precisely, we associate with each differential interaction net an event structure describing its reduction. We show how differential interaction nets are only able to generate confusion-free event structures, and we argue that this is a serious limitation in terms of the concurrent behaviours they may express. In fact, confusion is an extremely elementary phenomenon in concurrency (for example, it already appears in CCS with just prefixing and parallel composition) and we show how its presence is preserved by any encoding respecting the degree of distribution and the reduction semantics. We thus infer that no reasonably expressive process calculus may be satisfactorily encoded in differential interaction nets. We conclude with an analysis of one such encoding proposed by Ehrhard and Laurent, and argue that it does not contradict our claims, but rather supports them.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 28 , Special Issue 7: Differential Linear Logic, Nets and Other Quantitative and Parallel Approaches to Proof-Theory , August 2018 , pp. 1097 - 1125
Copyright
Copyright © Cambridge University Press 2016 

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