Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solving two-dimensional density classification problem with two
  probabilistic cellular automata   The density classification problem is one of the simplest yet non-trivial
computing tasks which seem to be ideally suitable for cellular automata (CA).
Unfortunately, there exists no one-dimensional two-state CA which classifies
binary strings according to their densities. If, however, in place of simple
cells one uses agents which change their behaviour from one rule to another
after a fixed number of iterations, the classification can be performed by the
traffic rule 184 and the majority rule 232. This two-rule solution cannot be
easily generalized to two (or higher) dimensions, because it critically depends
on a kinetic phase transition occurring in the rule 184. No rule exhibiting
analogous transition is known in two dimensions, most likely because no such
rule exists. We propose, therefore, to approach this problem form a slightly
different angle, namely by introducing a stochastic component into each of the
two rules. If one precedes each iteration of rule 184 by the stochastic "lane
changing rule," and each iteration of rule 232 by the stochastic "crowd
avoidance" rule, in the limit of infinitely many iterations the classification
can be performed correctly with probability 1. This solution can be described
either in the language of CA, or using the paradigm of agents which move and
proliferate on the 2D lattice, following probabilistic rules.

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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: nucl-th