Characterizations of complete residuated lattice-valued finite tree automata

This paper deals with the concept of complete residuated lattice-valued (referred to as L-valued) finite tree automata. In this regard, we first define an L-valued regular tree language, and then we prove a necessary and sufficient condition for the regularity of an L-valued tree language. Furthermore, we generalize the pumping lemma for L-valued finite tree automata (L-FTA). Afterwards, the behavior of L-FTA is addressed and some theorems are provided. Moreover, the existence of the minimal form of an L-FTA is considered. Finally, a minimization algorithm of the L-FTA is presented and its time complexity is analyzed.