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Undecidability Results for Monoids with Linear-Time Decidable Word Problems

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Algorithms and Computation (ISAAC 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1969))

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Abstract

Using a particularly adopted simulation of Turing machines by finite string-rewriting systems we show that all strong Markov properties are undecidable for the class C lin of finitely presented monoids with linear-time decidable word problems. Expanding on this construction it is then shown that also many other properties are undecidable for Clin, among them the property of having a context-free (or a regular) cross-section, the existence of a finite convergent presentation, and the homological and homotopical finiteness conditions left- and right-FPn (n≥3), left- and right-FP∞, FDT and FHT.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Kyoto-Sangyo University, 603, Kyoto, Japan

    Masashi Katsura

  2. Department of Information Science, Toho University, 274, Funabashi, Japan

    Yuji Kobayashi

  3. Fachbereich Mathematik/Informatik, Universität Kassel, 34109, Kassel, Germany

    Friedrich Otto

Authors
  1. Masashi Katsura
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  2. Yuji Kobayashi
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  3. Friedrich Otto
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Editor information

Editors and Affiliations

  1. Karlsruhe University, Germany

    Gerhard Goos

  2. Cornell University, NY, USA

    Juris Hartmanis

  3. Utrecht University, The Netherlands

    Jan van Leeuwen

  4. Academia Sinica, Institute of Information Science, 128 Academia Road, Section 2, Nankang, 115, Taipei, Taiwan, R.O.C.

    D. T. Lee

  5. Department of Computer Science and Akamai Technologies, University of Illinois at Urbana Champaign, 500 Technology Square, 02139, Cambridge, MA, USA

    Shang-Hua Teng

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© 2000 Springer-Verlag Berlin Heidelberg

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Katsura, M., Kobayashi, Y., Otto, F. (2000). Undecidability Results for Monoids with Linear-Time Decidable Word Problems. In: Goos, G., Hartmanis, J., van Leeuwen, J., Lee, D.T., Teng, SH. (eds) Algorithms and Computation. ISAAC 2000. Lecture Notes in Computer Science, vol 1969. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-40996-3_24

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  • DOI: https://doi.org/10.1007/3-540-40996-3_24

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  • Print ISBN: 978-3-540-41255-7

  • Online ISBN: 978-3-540-40996-0

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