Hankel Matrices for Weighted Visibly Pushdown Automata

TL;DR

This paper characterizes real-valued functions on nested words recognized by weighted visibly pushdown automata using Hankel matrices, extending previous logical characterizations in automata theory.

Contribution

It provides a new Hankel matrix-based characterization of functions recognized by weighted visibly pushdown automata, complementing existing logical approaches.

Findings

Hankel matrices characterize functions recognized by weighted visibly pushdown automata

Extends automata theory with a matrix-based characterization

Complements logical characterizations with a matrix approach

Abstract

Hankel matrices (aka connection matrices) of word functions and graph parameters have wide applications in automata theory, graph theory, and machine learning. We give a characterization of real-valued functions on nested words recognized by weighted visibly pushdown automata in terms of Hankel matrices on nested words. This complements C. Mathissen's characterization in terms of weighted monadic second order logic.