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The class of frontier testable (i.e., reverse definite) tree languages is characterized by a !inite set of pseudoidentities for tree algebras, which are introduced here for this characterization. An efficient algorithm is presented that decides whether a given tree automaton recognizes a frontier testable tree language. The algorithm runs in time O(mn3 + m*n*), where m is the cardinality of the alphabet and n is the number of states of the automaton. * *This is ofh called 'reverse deli&e', seedoi:10.1016/0304-3975(95)00131-x fatcat:5nsyzhg4lbdfbgtwjfkwcknwlq