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Breaking symmetries†

Published online by Cambridge University Press:  12 November 2014

KIRSTIN PETERS  and
UWE NESTMANN
KIRSTIN PETERS
Affiliation:
Technische Universität Berlin, Germany Email: kirstin.peters@tu-berlin.de, uwe.nestmann@tu-berlin.de
UWE NESTMANN
Affiliation:
Technische Universität Berlin, Germany Email: kirstin.peters@tu-berlin.de, uwe.nestmann@tu-berlin.de
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Abstract

A well-known result by Palamidessi tells us that πmix (the π-calculus with mixed choice) is more expressive than πsep (its subset with only separate choice). The proof of this result analyses their different expressive power concerning leader election in symmetric networks. Later on, Gorla offered an arguably simpler proof that, instead of leader election in symmetric networks, employed the reducibility of ‘incestual’ processes (mixed choices that include both enabled senders and receivers for the same channel) when running two copies in parallel. In both proofs, the role of breaking (initial) symmetries is more or less apparent. In this paper, we shed more light on this role by re-proving the above result – based on a proper formalization of what it means to break symmetries – without referring to another problem domain like leader election.

Both Palamidessi and Gorla rephrased their results by stating that there is no uniform and reasonable encoding from πmix into πsep. We indicate how their proofs can be adapted and exhibit the consequences of varying notions of uniformity and reasonableness. In each case, the ability to break initial symmetries turns out to be essential. Moreover, by abandoning the uniformity criterion, we show that there indeed is a reasonable encoding. We emphasize its underlying principle, which highlights the difference between breaking symmetries locally instead of globally.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 26 , Special Issue 6: Special Issue: Express'10 , September 2016 , pp. 1054 - 1106
Copyright
Copyright © Cambridge University Press 2014 

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Footnotes

†

Supported by the DFG (German Research Foundation), grant NE-1505/2-1.

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