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Non-solvable Groups Are Not in FO+MOD+MÂJ2[REG]

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Language and Automata Theory and Applications (LATA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5457))

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Abstract

Motivated by the open question whether \(\mbox{TC{$^0$}}=\mbox{NC{$^1$}}\) we consider the case of linear size TC0. We use the connections between circuits, logic, and algebra, in particular the characterization of \(\mbox{TC{$^0$}}\) in terms of finitely typed monoids. Applying algebraic methods we show that the word problem for finite non-solvable groups cannot be described by a FO+MOD+MAJ[REG] formula using only two variables. This implies a separation result of FO[REG]-uniform linear TC0 from linear NC1.

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Authors and Affiliations

  1. WSI - University of Tübingen, Sand 13, 72076, Tübingen, Germany

    Christoph Behle, Andreas Krebs & Stephanie Reifferscheid

Authors
  1. Christoph Behle
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  2. Andreas Krebs
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  3. Stephanie Reifferscheid
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Editor information

Editors and Affiliations

  1. Research Group on Mathematical Linguistics, Rovira i Virgili University, Av. Catalunya, 35, 43002, Tarragona, Spain

    Adrian Horia Dediu

  2. Research Group on Mathematical Linguistics, Universitat Rovira i Virgili, Tarragona, Spain

    Armand Mihai Ionescu

  3. European Research Council Executive Agency, 16 Place Rogier, 1210, Brussels, Belgium

    Carlos Martín-Vide

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© 2009 Springer-Verlag Berlin Heidelberg

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Behle, C., Krebs, A., Reifferscheid, S. (2009). Non-solvable Groups Are Not in FO+MOD+MÂJ2[REG]. In: Dediu, A.H., Ionescu, A.M., Martín-Vide, C. (eds) Language and Automata Theory and Applications. LATA 2009. Lecture Notes in Computer Science, vol 5457. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00982-2_11

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  • DOI: https://doi.org/10.1007/978-3-642-00982-2_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00981-5

  • Online ISBN: 978-3-642-00982-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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