Context-free multilanguages

TL;DR

This paper explores a generalized concept of context-free languages extended to multisets of words, aiming to track parsing counts, which could have implications for understanding ambiguous language structures.

Contribution

It introduces a novel extension of context-free languages to multisets, providing a framework to analyze multiple parse possibilities simultaneously.

Findings

Proposes a multiset-based generalization of context-free languages

Provides an informal yet rigorous treatment of the concept

Highlights potential applications in parsing ambiguous structures

Abstract

This article is a sketch of ideas that were once intended to appear in the author's famous series, "The Art of Computer Programming". He generalizes the notion of a context-free language from a set to a multiset of words over an alphabet. The idea is to keep track of the number of ways to parse a string. For example, "fruit flies like a banana" can famously be parsed in two ways; analogous examples in the setting of programming languages may yet be important in the future. The treatment is informal but essentially rigorous.