Weighted Languages Recognizable by Weighted Tree Automata

Abstract

Yields of recognizable weighted tree languages, yields of local weighted tree languages, and weighted context-free languages are related. It is shown that the following five classes of weighted languages are the same: (i) the class of weighted languages generated by plain weighted context-free grammars, (ii) the class of weighted languages recognized by plain weighted tree automata, (iii) the class of weighted languages recognized by deterministic and plain topdown weighted tree automata, (iv) the class of weighted languages recognized by deterministic and plain bottom-up weighted tree automata, and (v) the class of weighted languages determined by plain weighted local systems.