Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Back to the Coordinated Attack Problem   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.

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The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph