State complexity of k-parallel tree concatenation

Yo Sub Han, Sang Ki Ko, Kai Salomaa

Research output: Contribution to journalArticlepeer-review


We give an optimized construction of a tree automaton recognizing the k-parallel, k ≥ 1, tree concatenation of two regular tree languages. For tree automata with m and n states, respectively, the construction yields an upper bound (m+ 1 2)(n+1)· 2 nk -1 for the state complexity of k-parallel tree concatenation. We give a matching lower bound in the case k = 2. We conjecture that the upper bound is tight for all values of k. We also consider the special case where one of the tree languages is the set of all ranked trees and in this case establish a different tight state complexity bound for all values of k.

Original languageEnglish
Pages (from-to)185-199
Number of pages15
JournalFundamenta Informaticae
Issue number1-4
StatePublished - 2017


  • regular tree languages
  • state complexity
  • tree automata
  • tree concatenation


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