Language Classes Associated with Automata Over Matrix Groups
\"Ozlem Salehi, Flavio D'Alessandro, A.C.Cem Say

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.
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