Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On all things star-free   We investigate the star-free closure, which associates to a class of
languages its closure under Boolean operations and marked concatenation. We
prove that the star-free closure of any finite class and of any class of groups
languages with decidable separation (plus mild additional properties) has
decidable separation. We actually show decidability of a stronger property,
called covering. This generalizes many results on the subject in a unified
framework. A key ingredient is that star-free closure coincides with another
closure operator where Kleene stars are also allowed in restricted contexts.

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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: physics