We investigate weighted finite automata over strings and strong bimonoids. Such algebraic
structures satisfy the same laws as semirings except that no distributivity laws need to hold …

Weighted automata are classical finite automata in which the transitions carry weights. 7
These weights may model quantitative properties like the amount of resources needed for …

In automata theory, a fundamental result of Büchi and Elgot states that the recognizable
languages are precisely the ones definable by sentences of monadic second order logic …

The HOM-problem, which asks whether the image of a regular tree language under a tree
homomorphism is again regular, is known to be decidable by [Godoy, Gim\'enez …

The theory of fuzzy recognizable languages over bounded distributive lattices is presented
as a paradigm of recognizable formal power series. Due to the idempotency properties of …

We define a weighted monadic second order logic for unranked trees and the concept of
weighted unranked tree automata, and we investigate the expressive power of these two …

Graphs have a variety of uses in natural language processing, particularly as
representations of linguistic meaning. A deficit in this area of research is a formal framework …

Quantitative aspects of systems can be modeled by weighted automata. Here, we deal with
such automata running on finite trees. Usually, transitions are weighted with elements of a …

The HOM problem, which asks whether the image of a regular tree language under a given
tree homomorphism is again regular, is known to be decidable [Godoy & Giménez: The …

This is a book on weighted tree automata. We present the basic definitions and some of the
important results in a coherent form with full proofs. The concept of weighted tree automata …