Tree Generating Regular Systems

Trees are defined as mappings from tree structures (in the graph-theoretic sense) into sets of symbols. Regular systems are defined in which the production rules are of the form Φ → ψ , where Φ and ψ are trees. An application of a rule involves replacing a subtree Φ by the tree ψ . The main result is that the sets of trees generated by regular systems are exactly those that are accepted by tree automata. This generalizes a theorem of BUchi, proved for strings.

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