License: Creative Commons Attribution-NoDerivs 3.0 Unported license (CC BY-ND 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2009.1829
URN: urn:nbn:de:0030-drops-18297
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2009/1829/
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Gelade, Wouter ; Marquardt, Marcel ; Schwentick, Thomas

The Dynamic Complexity of Formal Languages

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Abstract

The paper investigates the power of the dynamic complexity classes DynFO, DynQF and DynPROP over string languages. The latter two classes contain problems that can be maintained using quantifier-free first-order updates, with and without auxiliary functions, respectively. It is shown that the languages maintainable in DynPROP exactly are the regular languages, even when allowing arbitrary precomputation. This enables lower bounds for DynPROP and separates DynPROP from DynQF and DynFO. Further, it is shown that any context-free language can be maintained in DynFO and a number of specific context-free languages, for example all Dyck-languages, are maintainable in DynQF. Furthermore, the dynamic complexity of regular tree languages is investigated and some results concerning arbitrary structures are obtained: there exist first-order definable properties which are not maintainable in DynPROP. On the other hand any existential first-order property can be maintained in DynQF when allowing precomputation.

BibTeX - Entry

@InProceedings{gelade_et_al:LIPIcs:2009:1829,
  author =	{Wouter Gelade and Marcel Marquardt and Thomas Schwentick},
  title =	{{The Dynamic Complexity of Formal Languages}},
  booktitle =	{26th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{481--492},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-09-5},
  ISSN =	{1868-8969},
  year =	{2009},
  volume =	{3},
  editor =	{Susanne Albers and Jean-Yves Marion},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2009/1829},
  URN =		{urn:nbn:de:0030-drops-18297},
  doi =		{10.4230/LIPIcs.STACS.2009.1829},
  annote =	{Keywords: Dynamic complexity, Regular languages, Context-free languages, DynFO}
}

Keywords: Dynamic complexity, Regular languages, Context-free languages, DynFO
Collection: 26th International Symposium on Theoretical Aspects of Computer Science
Issue Date: 2009
Date of publication: 19.02.2009

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