Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Profinite Techniques for Probabilistic Automata and the Markov Monoid
  Algorithm   We consider the value 1 problem for probabilistic automata over finite words:
it asks whether a given probabilistic automaton accepts words with probability
arbitrarily close to 1. This problem is known to be undecidable. However,
different algorithms have been proposed to partially solve it; it has been
recently shown that the Markov Monoid algorithm, based on algebra, is the most
correct algorithm so far. The first contribution of this paper is to give a
characterisation of the Markov Monoid algorithm. The second contribution is to
develop a profinite theory for probabilistic automata, called the prostochastic
theory. This new framework gives a topological account of the value 1 problem,
which in this context is cast as an emptiness problem. The above
characterisation is reformulated using the prostochastic theory, allowing us to
give a simple and modular proof.

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The categories of this paper are: hep-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg