Isomorphism of Regular Trees and Words

  • Markus Lohrey
  • Christian Mathissen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6756)


The complexity of the isomorphism problem for regular trees, regular linear orders, and regular words is analyzed. A tree is regular if it is isomorphic to the prefix order on a regular language. In case regular languages are represented by NFAs (DFAs), the isomorphism problem for regular trees turns out to be EXPTIME-complete (resp. P-complete). In case the input automata are acyclic NFAs (acyclic DFAs), the corresponding trees are (succinctly represented) finite trees, and the isomorphism problem turns out to be PSPACE-complete (resp. P-complete). A linear order is regular if it is isomorphic to the lexicographic order on a regular language. A polynomial time algorithm for the isomorphism problem for regular linear orders (and even regular words, which generalize the latter) given by DFAs is presented. This solves an open problem by Ésik and Bloom. A long version of this paper can be found in [18].


Polynomial Time Linear Order Regular Expression Polynomial Time Algorithm Regular Language 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Markus Lohrey
    • 1
  • Christian Mathissen
    • 1
  1. 1.Institut für InformatikUniversität LeipzigGermany

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