Characterization of Tree Automata Based on Quantum Logic

In this paper, we introduce the concept of non-deterministic tree automata based on quantum-valued logic whose underlying structure is a complete orthomodular lattice. First, we provide some concepts concerning quantum tree automata such as unary quantum acceptability predicate, and unary quantum regularity predicate. Next, some operations on quantum tree automata, including sum, product, concatenation and star are studied, and it is shown that the validity of many closure properties depends heavily upon the commutativity of the underlying logic. After that, the Kleene theorem about the equivalence of quantum regular tree expressions and quantum tree automata is proved. The developed results in this paper, clarify somewhat some essential distinctions between classical computation and quantum one.