We develop a general framework for weighted parsing which is built on top of grammar-based language models and employs multioperator monoids (M-monoids) as weight algebras. It generalizes previous work in that area, e.g., semiring parsing and weighted deductive parsing, and also covers applications outside the classical scope of parsing, e.g., algebraic dynamic programming. More specifically, we introduce weighted RTG-based language models (where RTG stands for regular tree grammar) and define the M-monoid parsing problem. We show an algorithm which is supposed to solve this problem and prove in detail that, for a large class of weighted RTG-based language models, the algorithm terminates and, indeed, solves this problem. We compare our algorithm with semiring parsing and weighted deductive parsing regarding applicability and complexity.

我们开发了一个加权解析的通用框架，该框架建立在基于语法的语言模型之上，并采用多算子幺半群（M-monoids）作为权重代数。它概括了该领域以前的工作，例如半环解析和加权演绎解析，还涵盖了经典解析范围之外的应用，例如代数动态规划。更具体地说，我们引入了基于加权 RTG 的语言模型（其中 RTG 代表正则树语法）并定义了M-monoid 解析问题. 我们展示了一个应该解决这个问题的算法，并详细证明，对于一大类基于加权 RTG 的语言模型，该算法终止并确实解决了这个问题。我们将我们的算法与半环解析和加权演绎解析在适用性和复杂性方面进行比较。