Dynamic Complexity of Regular Languages: Big Changes, Small Work
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Dynamic Complexity of Regular Languages: Big Changes, Small Work

Authors Felix Tschirbs, Nils Vortmeier, Thomas Zeume

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Author Details

Felix Tschirbs
  • Ruhr-Universität Bochum, Germany
Nils Vortmeier
  • Ruhr-Universität Bochum, Germany
Thomas Zeume
  • Ruhr-Universität Bochum, Germany

Acknowledgements

We are grateful to Jonas Schmidt and Thomas Schwentick for insightful discussions.

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Felix Tschirbs, Nils Vortmeier, and Thomas Zeume. Dynamic Complexity of Regular Languages: Big Changes, Small Work. In 31st EACSL Annual Conference on Computer Science Logic (CSL 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 252, pp. 35:1-35:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.CSL.2023.35

Abstract

Whether a changing string is member of a certain regular language can be maintained in the DynFO framework of Patnaik and Immerman: after changing the symbol at one position of the string, a first-order update formula can express - using additionally stored information - whether the resulting string is in the regular language.
We extend this and further known results by considering changes of many positions at once. We also investigate to which degree the obtained update formulas imply work-efficient parallel dynamic algorithms.

Subject Classification

ACM Subject Classification
  • Theory of computation → Complexity theory and logic
  • Theory of computation → Logic and databases
Keywords
  • dynamic descriptive complexity
  • regular languages
  • batch changes
  • work

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