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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/9918

Title: The Dynamic Complexity of Formal Languages
Authors: GELADE, Wouter
Marquardt, Marcel
Schwentick, Thomas
Issue Date: 2009
Publisher: Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany Internationales Begegnungs- und Forschungszentrum fuer Informatik (IBFI), Schloss Dagstuhl, Germany
Citation: Albers, Susanne & Marion, Jean-Yves (Ed.) Proceedings of the International Symposium on Theoretical Aspects of Computer Science. p. 481-492.
Series/Report: Dagstuhl Seminar Proceedings, 09001
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.
URI: http://hdl.handle.net/1942/9918
Link to publication: http://drops.dagstuhl.de/opus/volltexte/2009/1829
ISBN: 978-3-939897-09-5
Category: C1
Type: Proceedings Paper
Appears in Collections: Research publications

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