Some Hypergroups Induced By Tree Automata

In this paper, we present some connections between tree automaton theory and hyperstructure theory. In this regard, at first we construct some hyperoperations on the set of trees and, specially, prove that one of them creates a join space. Also, we define a hyperoperation on the states of a tree automaton and, based on the properties of the tree automaton, we show that the proposed hyperoperation creates different hypergroupoids. After that, we show that the state hypergroup of the direct product of tree automata is equal to the relational product of the state hypergroups corresponding to each of the tree automata. Finally, a hyperoperation on the set of alphabets is proposed and some hypergroupoids are derived.