A connection between concurrency and language theory

TL;DR

This paper establishes a fundamental link between classical language theory and process algebra by showing that three fixed point structures share the same valid equations, highlighting deep theoretical connections.

Contribution

It demonstrates that theories of context-free languages, regular tree languages, and process simulation equivalence share identical fixed point equations, revealing a new theoretical connection.

Findings

Shared fixed point equations across different language theories

Equivalence of fixed point structures in language and process algebra

Deepening the understanding of language theory and process algebra relationship

Abstract

We show that three fixed point structures equipped with (sequential) composition, a sum operation, and a fixed point operation share the same valid equations. These are the theories of (context-free) languages, (regular) tree languages, and simulation equivalence classes of (regular) synchronization trees (or processes). The results reveal a close relationship between classical language theory and process algebra.