How Many Cooks Spoil the Soup?

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9988)

Abstract

In this work, we study the following basic question: “How much parallelism does a distributed task permit?” Our definition of parallelism (or symmetry) here is not in terms of speed, but in terms of identical roles that processes have at the same time in the execution. We initiate this study in population protocols, a very simple model that not only allows for a straightforward definition of what a role is, but also encloses the challenge of isolating the properties that are due to the protocol from those that are due to the adversary scheduler, who controls the interactions between the processes. We (i) give a partial characterization of the set of predicates on input assignments that can be stably computed with maximum symmetry, i.e., \(\varTheta (N_{min})\), where \(N_{min}\) is the minimum multiplicity of a state in the initial configuration, and (ii) we turn our attention to the remaining predicates and prove a strong impossibility result for the parity predicate: the inherent symmetry of any protocol that stably computes it is upper bounded by a constant that depends on the size of the protocol.

Notes

Acknowledgements

We would like to thank Dimitrios Amaxilatis for setting up and running experiments for the evaluation of the observed symmetry.

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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of LiverpoolLiverpoolUK
  2. 2.Computer Technology Institute and Press “Diophantus” (CTI)PatrasGreece

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