### Abstract

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 language | English |
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Pages (from-to) | 185-199 |

Number of pages | 15 |

Journal | Fundamenta Informaticae |

Volume | 154 |

Issue number | 1-4 |

DOIs | |

Publication status | Published - 2017 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Algebra and Number Theory
- Information Systems
- Computational Theory and Mathematics

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## Cite this

Han, Y. S., Ko, S. K., & Salomaa, K. (2017). State complexity of k-parallel tree concatenation.

*Fundamenta Informaticae*,*154*(1-4), 185-199. https://doi.org/10.3233/FI-2017-1560