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Characterizing TC0 in Terms of Infinite Groups

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Abstract

We characterize the languages in TC0 = L(Maj[<,Bit]) and L(Maj[<]) as inverse morphic images of certain groups. Necessarily these are infinite, since nonregular sets are concerned. To limit the power of these infinite algebraic objects, we equip them with a finite type set and introduce the notion of a finitely typed (infinite) monoid. Following this approach we investigate type-respecting mappings and construct a new type of block product that more adequately deals with infinite monoids. We exhibit two classes of finitely typed groups which exactly characterize TC0 and L(Maj[<]) via inverse morphisms.

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Authors and Affiliations

  1. Wilhelm-Schickard-Institute, Sand 13, D-72076 Tubingen, Germany

    Andreas Krebs, Klaus-Jorn Lange & Stephanie Reifferscheid

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  1. Andreas Krebs
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  2. Klaus-Jorn Lange
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  3. Stephanie Reifferscheid
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Correspondence to Andreas Krebs, Klaus-Jorn Lange or Stephanie Reifferscheid.

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Krebs, A., Lange, KJ. & Reifferscheid, S. Characterizing TC0 in Terms of Infinite Groups. Theory Comput Syst 40, 303–325 (2007). https://doi.org/10.1007/s00224-006-1310-2

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  • DOI: https://doi.org/10.1007/s00224-006-1310-2

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