Proving Parikh's theorem using Chomsky-Schutzenberger theorem

TL;DR

This paper offers a new proof of Parikh's theorem by leveraging the Chomsky-Schutzenberger representation theorem and linear algebra, avoiding traditional formal language theory tools.

Contribution

It provides a novel proof of Parikh's theorem using only the Chomsky-Schutzenberger theorem and linear algebra, simplifying the proof process.

Findings

New proof of Parikh's theorem established

Proof relies solely on Chomsky-Schutzenberger theorem and linear algebra

Simplifies understanding of Parikh's theorem

Abstract

Parikh theorem was originally stated and proved by Rohkit Parikh in MIT research report in 1961. Many different proofs of this classical theorems were produced then; our goal is to give another proof using Chomsky-Schutzenberger representation theorem. We present the proof which doesn't use any formal language theory tool at all except the representation theorem, just some linear algebra.