### 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 Jan 1 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*Fundamenta Informaticae*,

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

}

*Fundamenta Informaticae*, vol. 154, no. 1-4, pp. 185-199. https://doi.org/10.3233/FI-2017-1560

**State complexity of k-parallel tree concatenation.** / Han, Yo-Sub; Ko, Sang Ki; Salomaa, Kai.

Research output: Contribution to journal › Article

TY - JOUR

T1 - State complexity of k-parallel tree concatenation

AU - Han, Yo-Sub

AU - Ko, Sang Ki

AU - Salomaa, Kai

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85027310144&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85027310144&partnerID=8YFLogxK

U2 - 10.3233/FI-2017-1560

DO - 10.3233/FI-2017-1560

M3 - Article

VL - 154

SP - 185

EP - 199

JO - Fundamenta Informaticae

JF - Fundamenta Informaticae

SN - 0169-2968

IS - 1-4

ER -