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Documents authored by Gelade, Wouter

Document
DOI: 10.4230/LIPIcs.STACS.2009.1829
The Dynamic Complexity of Formal Languages

Authors: Wouter Gelade, Marcel Marquardt, and Thomas Schwentick

Published in: LIPIcs, Volume 3, 26th International Symposium on Theoretical Aspects of Computer Science (2009)

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.
Cite as

Wouter Gelade, Marcel Marquardt, and Thomas Schwentick. The Dynamic Complexity of Formal Languages. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 481-492, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{gelade_et_al:LIPIcs.STACS.2009.1829,
  author =	{Gelade, Wouter and Marquardt, Marcel and Schwentick, Thomas},
  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 =	{Albers, Susanne and Marion, Jean-Yves},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.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}
}
Document
DOI: 10.4230/LIPIcs.STACS.2008.1354
Succinctness of the Complement and Intersection of Regular Expressions

Authors: Wouter Gelade and Frank Neven

Published in: LIPIcs, Volume 1, 25th International Symposium on Theoretical Aspects of Computer Science (2008)

Abstract
We study the succinctness of the complement and intersection of regular expressions. In particular, we show that when constructing a regular expression defining the complement of a given regular expression, a double exponential size increase cannot be avoided. Similarly, when constructing a regular expression defining the intersection of a fixed and an arbitrary number of regular expressions, an exponential and double exponential size increase, respectively, can in worst-case not be avoided. All mentioned lower bounds improve the existing ones by one exponential and are tight in the sense that the target expression can be constructed in the corresponding time class, i.e., exponential or double exponential time. As a by-product, we generalize a theorem by Ehrenfeucht and Zeiger stating that there is a class of DFAs which are exponentially more succinct than regular expressions, to a fixed four-letter alphabet. When the given regular expressions are one-unambiguous, as for instance required by the XML Schema specification, the complement can be computed in polynomial time whereas the bounds concerning intersection continue to hold. For the subclass of single-occurrence regular expressions, we prove a tight exponential lower bound for intersection.
Cite as

Wouter Gelade and Frank Neven. Succinctness of the Complement and Intersection of Regular Expressions. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 325-336, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{gelade_et_al:LIPIcs.STACS.2008.1354,
  author =	{Gelade, Wouter and Neven, Frank},
  title =	{{Succinctness of the Complement and Intersection of Regular Expressions}},
  booktitle =	{25th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{325--336},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-06-4},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{1},
  editor =	{Albers, Susanne and Weil, Pascal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1354},
  URN =		{urn:nbn:de:0030-drops-13541},
  doi =		{10.4230/LIPIcs.STACS.2008.1354},
  annote =	{Keywords: }
}
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