Tree Automata and Essential Input Variables

We introduce the essential inputs (variables) for terms (trees) and tree automata. It is proved that if an input xi is essential for a tree t and an automaton A then there is a chain of subtrees connecting xi with the root of t such that xi is essential for each subtree belonging to this chain. There are investigations which treat some rules for removing and adding of fictive (non-essential) inputs of a term. We consider a new point of view of minimization of tree-automata and tree-languages. Such minimization is realized by a procedure (algorithm). AMS, subject classification: 03D05, 68Q70, 03D15, 06B25