TREE AUTOMATA BASED ON COMPLETE RESIDUATED LATTICE-VALUED LOGIC: REDUCTION ALGORITHM an‎d DECISION PROBLEMS

In this paper, at rst we dene the concepts of response function and accessible states of a complete residuated lattice-valued (for simplicity we write L-valued) tree automaton with a threshold c: Then, related to these concepts, we prove some lemmas and theorems that are applied in considering some decision problems such as niteness-value and emptiness-value of recognizable tree languages. Moreover, we propose a reduction algorithm for L-valued tree automata with a threshold c: The goal of reducing an L-valued tree automaton is to obtain an L-valued tree automaton with reduced number of states all of which are accessible, in addition it recognizes the same language as the rst one given. We compare our algorithm with some other algorithms in the literature. Finally, utilizing the obtained results, we consider some fundamental decision problems for L-valued tree automata including the membership-value, the emptiness-value, the niteness-value, the intersectionvalue and the equivalence-value problems.