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The Dynamic Complexity of Formal Languages Gelade, Wouter Marquardt, Marcel Schwentick, Thomas Dynamic complexity Regular languages Context-free languages DynFO 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Wouter Gelade and Marcel Marquardt and Thomas Schwentick 2009 Is Part Of LIPIcs, Volume 3, 26th International Symposium on Theoretical Aspects of Computer Science (2009) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2009.1829 urn:nbn:de:0030-drops-18297 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1829 eng https://creativecommons.org/licenses/by-nd/3.0/legalcode