On the Recognition Capacity of Abelian Graph Automata (European Journal of Pure and Applied Mathematics, 2025)
This paper explores the recognition capacity of both unitary and non-unitary Abelian graph automata through the algebraic structure of graphoids. We investigate for the first time in the literature the recognition mechanism of non-unitary Abelian graph automata and prove that they can recognize graph languages which are beyond the recognition power of unitary graph automata. Consequently, we establish that the class of graph languages recognized by unitary automata is strictly contained within the class of those recognized by Abelian graph automata. These results manifest a proper hierarchy among graph automata classes and provide new insights into the recognition capabilities of graph automata.