Pushing for weighted tree automata

Abstract

Explicit pushing for weighted tree automata over semifields is introduced. A careful selection of the pushing weights allows a normalization of bottom-up deterministic weighted tree automata. Automata in the obtained normal form can be minimized by a simple transformation into an unweighted automaton followed by unweighted minimization. This generalizes results of Mohri and Eisner for deterministic weighted string automata to the tree case. Moreover, the new strategy can also be used to test equivalence of two bottom-up deterministic weighted tree automata M1 and M2 in time O(|M |log|Q|), where |M| = |M1| + |M2| and |Q| is the sum of the number of states of M1 and M2. This improves the previously best running time O(|M1|·|M2|). © 2011 Springer-Verlag GmbH.