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Dense Completeness

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Developments in Language Theory (DLT 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7410))

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Abstract

We introduce dense completeness, which gives tighter connection between formal language classes and complexity classes than the usual notion of completeness. A family of formal languages \(\mathcal F\) is densely complete in a complexity class \(\mathcal C\) iff \({\mathcal F}\subseteq{\mathcal C}\) and for each \(C \in{\mathcal C}\) there is an \(F \in{\mathcal F}\) such that F is many-one equivalent to C.

For AC 0-reductions we show the following results: the family CFL of context-free languages is densely complete in the complexity class SAC1. Moreover, we show that the indexed languages are densely complete in NP and the nondeterministic one-counter languages are densely complete in NL. On the other hand, we prove that the regular languages are not densely complete in NC1.

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Author information

Authors and Affiliations

  1. University of Tübingen, Germany

    Andreas Krebs & Klaus-Jörn Lange

Authors
  1. Andreas Krebs
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  2. Klaus-Jörn Lange
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Editor information

Editors and Affiliations

  1. Deptartment of Electrical Engineering, National Taiwan University, 106, Taipei, Taiwan

    Hsu-Chun Yen

  2. Department of Computer Science, University of California, 93106, Santa Barbara, CA, USA

    Oscar H. Ibarra

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Krebs, A., Lange, KJ. (2012). Dense Completeness. In: Yen, HC., Ibarra, O.H. (eds) Developments in Language Theory. DLT 2012. Lecture Notes in Computer Science, vol 7410. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31653-1_17

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  • DOI: https://doi.org/10.1007/978-3-642-31653-1_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31652-4

  • Online ISBN: 978-3-642-31653-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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