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On Distinguishing NC\(^1\) and NL

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Book cover Developments in Language Theory (DLT 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9168))

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Abstract

We obtain results within the area of dense completeness, which describes a close relation between families of formal languages and complexity classes. Previously we were able show that this relation exists between counter languages and \(\mathbf {NL}\) but not between the regular languages and \(\mathbf {NC^1}\).

We narrow the gap between the regular languages and the counter languages by considering visibly counter languages. It turns out that they are not densely complete for \(\mathbf {NC^1}\). At the same time we found a restricted counter automaton model which is densely complete for \(\mathbf {NL}\).

Besides counter automata we show more positive examples in terms of L-systems.

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Authors and Affiliations

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

    Andreas Krebs, Klaus-Jörn Lange & Michael Ludwig

Authors
  1. Andreas Krebs
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  2. Klaus-Jörn Lange
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  3. Michael Ludwig
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Corresponding author

Correspondence to Klaus-Jörn Lange .

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Editors and Affiliations

  1. University of Liverpool, Liverpool, United Kingdom

    Igor Potapov

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Krebs, A., Lange, KJ., Ludwig, M. (2015). On Distinguishing NC\(^1\) and NL. In: Potapov, I. (eds) Developments in Language Theory. DLT 2015. Lecture Notes in Computer Science(), vol 9168. Springer, Cham. https://doi.org/10.1007/978-3-319-21500-6_27

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  • DOI: https://doi.org/10.1007/978-3-319-21500-6_27

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21499-3

  • Online ISBN: 978-3-319-21500-6

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