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Automata, Languages and Programming pp 361–371Cite as

Computing LOGCFL Certificates

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1644))

Abstract

By results of Ruzzo [13], the complexity class LOGCFL can be characterized as the class of languages accepted by alternating Turing Machines (ATMs) which use logarithmic space and have polynomially sized accepting computation trees. We show that for each such ATM M recognizing a language A in LOGCFL, it is possible to construct an LLOGCFL transducer TM such that TM on input w ∈ A outputs an accepting tree for M on w. It follows that computing single LOGCFL certificates is feasible in functional AC1 and is thus highly parallelizable. Wanke [17] has recently shown that for any fixed k, deciding whether the treewidth of a graph is at most k is in the complexity-class LOGCFL. As an application of our general result, it follows that the task of computing a tree-decomposition for a graph of constant treewidth is in functional LOGCFL, and thus in AC1. Similar results apply to many other important search problems corresponding to decision problems in LOGCFL.

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Author information

Authors and Affiliations

  1. Institut für Informationssysteme, Technische Universität Wien, Austria

    Georg Gottlob, Nicola Leone & Francesco Scarcello

Authors
  1. Georg Gottlob
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  2. Nicola Leone
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  3. Francesco Scarcello
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Editor information

Editors and Affiliations

  1. Institute for Computer Science, Academy of Sciences of the Czech Republic, Pod vodarenskou vezi 2, 182 07, Prague 8 - Liben, Czech Republic

    Jirí Wiedermann

  2. ILLC-WINS-University of Amsterdam, Plantage Muidergracht 24, 1018, TV, Amsterdam, The Netherlands

    Peter van Emde Boas

  3. BRICS, Department of Computer Science, University of Aarhus, Ny Munkegade, Bldg. 540, DK, 8000, Aarhus C, Denmark

    Mogens Nielsen

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© 1999 Springer-Verlag Berlin Heidelberg

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Gottlob, G., Leone, N., Scarcello, F. (1999). Computing LOGCFL Certificates. In: Wiedermann, J., van Emde Boas, P., Nielsen, M. (eds) Automata, Languages and Programming. Lecture Notes in Computer Science, vol 1644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48523-6_33

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  • DOI: https://doi.org/10.1007/3-540-48523-6_33

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66224-2

  • Online ISBN: 978-3-540-48523-0

  • eBook Packages: Springer Book Archive

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