Formal languages and groups as memory

TL;DR

This paper explores finite automata enhanced with memory registers from monoids or groups, providing new foundational results and illustrating their application through a group-theoretic proof of a key formal language theory theorem.

Contribution

It introduces new foundational results for automata with group or monoid memory and offers a novel group-theoretic proof of a classical theorem.

Findings

New results on automata with group/memory registers

A group-theoretic interpretation of a key formal language theorem

Enhanced understanding of automata and formal languages

Abstract

We present an exposition of the theory of finite automata augmented with a multiply-only register storing an element of a given monoid or group. Included are a number of new results of a foundational nature. We illustrate our techniques with a group-theoretic interpretation and proof of a key theorem of Chomsky and Schutzenberger from formal language theory.