Abstract

We consider regular languages of ranked labeled trees. We give an algebraic characterization of the regular languages over such trees that are definable in first-order logic in the language of labeled graphs. These languages are the analog on ranked trees of the “locally threshold testable” languages on strings. We show that this characterization yields a decision procedure for determining whether a regular collection of trees is first-order definable: the procedure is polynomial time in the minimal automaton presenting the regular language.

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