Partially-commutative context-free languages

TL;DR

This paper explores the properties of partially-commutative context-free languages (PCCFL), a class extending CFLs with commutativity, analyzing automata models, stability under operations, and relationships with other language classes.

Contribution

It provides a comprehensive survey of PCCFL, introduces a natural automaton model, and establishes stability and expressiveness relations with related language classes.

Findings

PCCFL is stable under shuffle and homomorphic images.

Introduces stateless multi-pushdown automata for PCCFL.

Establishes relationships between PCCFL, CFL with shuffle, and trace-closures.

Abstract

The paper is about a class of languages that extends context-free languages (CFL) and is stable under shuffle. Specifically, we investigate the class of partially-commutative context-free languages (PCCFL), where non-terminal symbols are commutative according to a binary independence relation, very much like in trace theory. The class has been recently proposed as a robust class subsuming CFL and commutative CFL. This paper surveys properties of PCCFL. We identify a natural corresponding automaton model: stateless multi-pushdown automata. We show stability of the class under natural operations, including homomorphic images and shuffle. Finally, we relate expressiveness of PCCFL to two other relevant classes: CFL extended with shuffle and trace-closures of CFL. Among technical contributions of the paper are pumping lemmas, as an elegant completion of known pumping properties of regular languages, CFL and commutative CFL.