A Medvedev Characterization of Recognizable Tree Series

Weighted Tree Generating Regular Systems and Crisp-Determinization of Weighted Tree Automata

“…Furthermore, similarly to the unweighted case, additional concepts were invented and shown to be equivalent to wta, see e.g., weighted regular tree grammars [7] and the Kleene theorem for wta [7,29]; monadic secondorder logic and the Büchi-Elgot-Trakhtenbrot's theorem for recognizable weighted tree languages [31,40] (cf. [25][26][27] for the string case); and weighted representable tree languages [51,52]. It is also known that each each weighted tree language recognized by a wta is the image of a local weighted tree language under a deterministic tree relabeling [38].…”