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 $|Q| \cdot |\Gamma|$.

翻译：加权推下自动数据(WPDAs)是许多自然语言处理任务的核心,例如基于语法的统计机器翻译和基于过渡性依赖分析。由于大多数现有的动态编程算法是为无上下文语法(CFGs)设计的,因此PDAs的算法往往采用PDA-to-CFG转换法。在本文中,我们开发了直接对WPDAs运作的新型算法。我们的算法受到Lang的算法的启发,但使用更笼统的自下而上的自动数据定义,或者将空间需求减少一个因子(堆叠字母的大小) $++Gamma, 或者将运行时间减少一个因子(州数) $+++$。当运行与Lang的算法一样的PDAs类时,我们的算法不仅以$+Gamma $的系数提高了空间效率,而且以 $\cdot {Gamma $的系数提高了时间效率。