Skip to Main content Skip to Navigation
Conference papers

The Dynamic complexity of formal languages

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.
Complete list of metadata

Cited literature [20 references]  Display  Hide  Download

https://hal.inria.fr/inria-00359755
Contributor : Publications Loria <>
Submitted on : Monday, February 9, 2009 - 12:11:36 PM
Last modification on : Friday, February 19, 2021 - 5:38:02 PM
Long-term archiving on: : Tuesday, June 8, 2010 - 10:06:00 PM

File

40-gelade.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : inria-00359755, version 1

Collections

Citation

Wouter Gelade, Marcel Marquardt, Thomas Schwentick. The Dynamic complexity of formal languages. 26th International Symposium on Theoretical Aspects of Computer Science - STACS 2009, Feb 2009, Freiburg, Germany. pp.481-492. ⟨inria-00359755⟩

Share

Metrics

Record views

248

Files downloads

568