A Note on Recognizable Sets of Unranked and Unordered Trees

Recognizable sets of unranked, unordered trees have been introduced in Courcelle [C89] in a Myhill-Nerode [N58] style of inverse homomorphisms of suitable finite magmas. This is equivalent of being the the union of some congruence classes of a congruence of finite index. We will add to the well-known concept of regular tree grammars a handling of nodes labeled with ǫ. With this rather unconventional but nevertheless natural treatment of the ”empty node” the class of languages generated by regular trees grammars becomes equivalent to Courcelles class of recognizable sets of unranked, unordered trees.

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