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Back to the Coordinated Attack Problem

Published online by Cambridge University Press:  09 July 2021

Emmanuel Godard Open the ORCID record for Emmanuel Godard [Opens in a new window]  and
Eloi Perdereau
Emmanuel Godard*
Affiliation:
Laboratoire d’Informatique et Systèmes, Aix-Marseille Université – CNRS (UMR 7020), Marseille, France
Eloi Perdereau
Affiliation:
Laboratoire d’Informatique et Systèmes, Aix-Marseille Université – CNRS (UMR 7020), Marseille, France
*
*Corresponding author Email: [email protected]
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Abstract

We consider the well-known Coordinated Attack Problem, where two generals have to decide on a common attack, when their messengers can be captured by the enemy. Informally, this problem represents the difficulties to agree in the presence of communication faults. We consider here only omission faults (loss of message), but contrary to previous studies, we do not to restrict the way messages can be lost, i.e., we make no specific assumption, we use no specific failure metric. In the large subclass of message adversaries where the double simultaneous omission can never happen, we characterize which ones are obstructions for the Coordinated Attack Problem. We give two proofs of this result. One is combinatorial and uses the classical bivalency technique for the necessary condition. The second is topological and uses simplicial complexes to prove the necessary condition. We also present two different Consensus algorithms that are combinatorial (resp. topological) in essence. Finally, we analyze the two proofs and illustrate the relationship between the combinatorial approach and the topological approach in the very general case of message adversaries. We show that the topological characterization gives a clearer explanation of why some message adversaries are obstructions or not. This result is a convincing illustration of the power of topological tools for distributed computability.

Keywords

Distributed systemsfault-tolerancemessage-passingsynchronous systemscoordinated attack problemtwo generals problemtwo armies problemconsensusmessage adversariesomission faultsdistributed computabilitysimplicial complexestopological methods
Type
Paper
Information
Mathematical Structures in Computer Science , Volume 30 , Issue 10 , November 2020 , pp. 1089 - 1113
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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