Query Learning of Regular Tree Languages: How to Avoid Dead States

MAT learners for tree series: an abstract data type and two realizations

“…This process terminates when the equivalence has converged to the Myhill-Nerode equivalence. The learners in [12,13,19] are all very similar. Following Angluin's original approach, they maintain an observation table, whose rows are indexed by trees representing the states and transitions of an automaton.…”

“…Angluin's original model was designed for learning ordinary deterministic finite automata (dfa). Its first generalization to bottom-up tree automata was proposed by Sakakibara in [21] and later improved in [12].…”

“…The first extension to dwta is found in [13]. This learner generalizes the learner in [12] from bottom-up tree automata to 'all-accepting' dwta, and was in turn extended to general dwta in [19]. In both cases, the weight structure is a semifield (i.e., a semiring, in which multiplicative inverses exist).…”

Learning Tree Languages

“…The point is that several decidability questions and related tasks can become significantly harder for trees as compared to strings. For instance, useless states pose no problem for string processing finite automata, but they do so for trees; see [67]. Also, there are certain intricacies that make a simple translation from the string to the tree case sometimes an error-prone task, as certified by the learner for representative samples and membership queries as discussed in [24,108].…”

“…He considered skeletal languages, that is, the parse trees of context-free languages in which all internal nodes are unlabeled [131]. Drewes and Högberg considered regular tree languages in general [66], and proved that it is possible to avoid useless states in the inference process [67]. By doing so, the automaton A becomes a language-equivalent partial automaton with potentially exponentially fewer states.…”