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On Markov's Undecidability Theorem for Integer Matrices

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Abstract

We study a problem considered originally by A. Markov in 1947: Given two finitely generated matrix semigroups, determine whether or not they contain a common element. This problem was proved undecidable by Markov for 4 x 4 matrices, even in a very restrict form, and for 3 x 3 matrices by Krom in 1981. Here we give a new proof in the 3 x 3 case which gives undecidability in an almost as restricted form as the result of Markov.

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Authors and Affiliations

  1. Department of Mathematics and TUCS, Turku Centre for Computer Science, University of Turku, FIN-20014 Turku, Finland

    Vesa Halava & Tero Harju

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  1. Vesa Halava
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  2. Tero Harju
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Correspondence to Vesa Halava or Tero Harju.

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Halava, V., Harju, T. On Markov's Undecidability Theorem for Integer Matrices. Semigroup Forum 75, 173–180 (2007). https://doi.org/10.1007/s00233-007-0714-x

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  • DOI: https://doi.org/10.1007/s00233-007-0714-x

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