Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Learning to Count up to Symmetry   In this paper we develop the theory of how to count, in thin concurrent
games, the configurations of a strategy witnessing that it reaches a certain
configuration of the game. This plays a central role in many recent
developments in concurrent games, whenever one aims to relate concurrent
strategies with weighted relational models. The difficulty, of course, is
symmetry: in the presence of symmetry many configurations of the strategy are,
morally, different instances of the same, only differing on the inessential
choice of copy indices. How do we know which ones to count? The purpose of the
paper is to clarify that, uncovering many strange phenomena and fascinating
pathological examples along the way. To illustrate the results, we show that a
collapse operation to a simple weighted relational model simply counting
witnesses is preserved under composition, provided the strategies involved do
not deadlock.

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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con