文章基本信息

标题：The Dynamic Complexity of Formal Languages
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作者：Wouter Gelade ; Marcel Marquardt ; Thomas Schwentick 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2009
卷号：3
页码：481-492
DOI：10.4230/LIPIcs.STACS.2009.1829
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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.
关键词：Dynamic complexity; Regular languages; Context-free languages; DynFO