TL;DR
This paper introduces Cayley Automata and Cayley Automaton semigroups, explores their properties, and addresses questions about their isomorphism with original semigroups and dual constructions.
Contribution
It presents the concept of Cayley Automata, investigates their semigroups, and answers a specific open question about dual constructions in automaton semigroups.
Findings
Characterization of semigroups isomorphic to their Cayley Automaton semigroups
Results for special classes of semigroups
Resolution of Cain's question on dual constructions
Abstract
After reviewing automaton semigroups, we introduce Cayley Automata and the corresponding Cayley Automaton semigroups. We investigate which semigroups are isomorphic to their Cayley Automaton semigroup and give some results for special classes of semigroups. We answer a question posed by Cain relating to the dual construction.
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