State Complexity of k-Parallel Tree Concatenation
Yo-Sub Han, Sang‐Ki Ko, Kai Salomaa · Fundamenta Informaticae · 2017
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+12)(n+1)⋅2nk−1 for the state complexity of k-parallel tree concat enation. 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.