Weighted Parsing for Grammar-Based Language Models over Multioperator Monoids

Abstract: We develop a general framework for weighted parsing which is built on top of grammar-based LLMs and employs multioperator monoids as weight algebras. It generalizes previous work in that area (semiring parsing, weighted deductive parsing) and also covers applications outside the classical scope of parsing, e.g., algebraic dynamic programming. We show an algorithm for weighted parsing and, for a large class of weighted grammar-based LLMs, we prove formally that it terminates and is correct.