Minimization of Deterministic Fuzzy Tree Automata

Until now, some methods for minimizing deterministic fuzzy finite tree automata (DFFTA) and weighted tree automata have been established by researchers. Those methods are language preserving, but the behavior of original automata and minimized one may be different. This paper, considers both language preserving and behavior preserving in minimization process. We drive Myhill-Nerode kind theorems corresponding to each proposed method and introduce PTIME algorithms for behaviorally and linguistically minimization. The proposed minimization algorithms are based on two main steps. The first step includes finding dependency between equivalency of states, according to the set of transition rules of DFFTA, and making merging dependency graph (MDG). The second step is refinement of MDG and making minimization equivalency set (MES). Additionally, behavior preserving minimization of DFFTA requires a pre-processing for modifying fuzzy membership grade of rules and final states, which is called normalization.