Weighted Tree Automata and Tree Transducers

Abstract

We survey some important results for weighted tree automata and weighted tree transducers over finite ranked trees and semirings as weight structure. In particular, we address closure properties of the class of recognizable tree series, results on the support of such tree series, the determinization of weighted tree automata, pumping lemmata and decidability results, and finite algebraic characterizations of recognizable tree series. We discuss the equivalence between recognizable tree series and equational, rational, and MSO-definable tree series, and we present a comparison of several other models of recognizability. For weighted tree transducers we show composition and decomposition results, an inclusion diagram of some fundamental classes of tree series transformations, and hierarchies obtained by composing weighted tree transducers. We also discuss other models of weighted tree transducers.