Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Upper and Lower Bounds on the Length of Alternating Towers   A tower between two regular languages is a sequence of strings such that all
strings on odd positions belong to one of the languages, all strings on even
positions belong to the other language, and each string can be embedded into
the next string in the sequence. It is known that if there are towers of any
length, then there also exists an infinite tower. We investigate upper and
lower bounds on the length of finite towers between two regular languages with
respect to the size of the automata representing the languages in the case
there is no infinite tower. This problem is relevant to the separation problem
of regular languages by piecewise testable languages.

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The categories of this paper are: stat
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The categories of this paper are: hep-ph
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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: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: astro-ph