Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homonym Population Protocols   The population protocol model was introduced by Angluin \emph{et al.} as a
model of passively mobile anonymous finite-state agents. This model computes a
predicate on the multiset of their inputs via interactions by pairs. The
original population protocol model has been proved to compute only semi-linear
predicates and has been recently extended in various ways. In the community
protocol model by Guerraoui and Ruppert, agents have unique identifiers but may
only store a finite number of the identifiers they already heard about. The
community protocol model provides the power of a Turing machine with a $O(n\log
n)$ space. We consider variations on the two above models and we obtain a whole
landscape that covers and extends already known results. Namely, by considering
the case of homonyms, that is to say the case when several agents may share the
same identifier, we provide a hierarchy that goes from the case of no
identifier (population protocol model) to the case of unique identifiers
(community protocol model). We obtain in particular that any Turing Machine on
space $O(\log^{O(1)} n)$ can be simulated with at least $O(\log^{O(1)} n)$
identifiers, a result filling a gap left open in all previous studies. Our
results also extend and revisit in particular the hierarchy provided by
Chatzigiannakis \emph{et al.} on population protocols carrying Turing Machines
on limited space, solving the problem of the gap left by this work between
per-agent space $o(\log \log n)$ (proved to be equivalent to population
protocols) and $O(\log n)$ (proved to be equivalent to Turing machines).

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The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: math