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Undecidable Problems for Probabilistic Automata of Fixed Dimension

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Abstract

We prove that several problems associated with probabilistic finite automata are undecidable for automata whose number of input letters and number of states are fixed. As a corollary of one of our results we prove that the problem of determining if the set of all products of two 47 × 47 matrices with nonnegative rational entries is bounded is undecidable.

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  1. Division of Applied Mathematics, University of Louvain, Bâtiment Euler, Avenue Georges Lemaitre 4, B-1348 Louvain-la-Neuve, Belgium blondel@inma.ucl.ac.be,canterini@inma.ucl.ac.be, BE

    Blondel &  Canterini

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  1. Blondel
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  2. Canterini
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Blondel, Canterini Undecidable Problems for Probabilistic Automata of Fixed Dimension . Theory Comput. Systems 36, 231–245 (2003). https://doi.org/10.1007/s00224-003-1061-2

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  • DOI: https://doi.org/10.1007/s00224-003-1061-2

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