Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Automata Theoretic Approach to the Zero-One Law for Regular
  Languages: Algorithmic and Logical Aspects   A zero-one language L is a regular language whose asymptotic probability
converges to either zero or one. In this case, we say that L obeys the zero-one
law. We prove that a regular language obeys the zero-one law if and only if its
syntactic monoid has a zero element, by means of Eilenberg's variety theoretic
approach. Our proof gives an effective automata characterisation of the
zero-one law for regular languages, and it leads to a linear time algorithm for
testing whether a given regular language is zero-one. In addition, we discuss
the logical aspects of the zero-one law for regular languages.

18
The categories of this paper are: econ
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The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
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The categories of this paper are: eess
31
The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
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The categories of this paper are: math
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int