Investigates the regularity of tree languages accepted by probabilistic tree automata at isolated cut-points, implying structural insights into their classification.
In this paper we introduce a probabilistic tree automaton by extending the notion of a tree automaton. Let A be a probabilistic tree automaton and RT(A;λ) be a congruence relation defined by a tree language T(A;λ) which a probabilistic tree automaton A accepts with a cut-point λ, 0≤λ<1. We prove that if λ is an isolated cut-point then the number of equivalence classes of RT(A;λ) is finite, that is, T(A;λ) is regular.
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Sugino et al. (1982) studied this question.
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