Algorithms for Weighted Pushdown Automata

TL;DR

This paper introduces new algorithms for weighted pushdown automata that operate directly on them, improving space and time efficiency over existing methods inspired by Lang's algorithm.

Contribution

The paper presents novel algorithms for WPDAs that reduce space and runtime complexity, avoiding the need for PDA-to-CFG conversion.

Findings

Algorithms are more space-efficient by a factor of |||

Algorithms are more time-efficient by a factor of |Q| * |||

Operate directly on WPDAs, improving efficiency over existing methods.

Abstract

Weighted pushdown automata (WPDAs) are at the core of many natural language processing tasks, like syntax-based statistical machine translation and transition-based dependency parsing. As most existing dynamic programming algorithms are designed for context-free grammars (CFGs), algorithms for PDAs often resort to a PDA-to-CFG conversion. In this paper, we develop novel algorithms that operate directly on WPDAs. Our algorithms are inspired by Lang's algorithm, but use a more general definition of pushdown automaton and either reduce the space requirements by a factor of $|\Gamma|$ (the size of the stack alphabet) or reduce the runtime by a factor of more than $|Q|$ (the number of states). When run on the same class of PDAs as Lang's algorithm, our algorithm is both more space-efficient by a factor of $|\Gamma|$ and more time-efficient by a factor of $|Q| \cdot |\Gamma|$.