Language Classes Associated with Automata Over Matrix Groups

TL;DR

This paper explores the computational capabilities of automata over matrix groups, especially focusing on those with polynomial growth, and summarizes recent and new findings in this area.

Contribution

It provides a comprehensive overview of language classes recognized by group automata over matrix groups, including new results on time-bounded automata with polynomial growth groups.

Findings

Automata over matrix groups recognize specific language classes.

Polynomial growth groups influence the computational power of automata.

New results on time-bounded automata with polynomial growth groups.

Abstract

We investigate the language classes recognized by group automata over matrix groups. We present a summary of the results obtained so far together with a number of new results. We look at the computational power of time-bounded group automata where the group under consideration has polynomial growth.