On the 3-state Mealy Automata over an m-symbol Alphabet of Growth Order [ n ^{{\log n}/{2 \log m}} ]

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/110014We consider the sequence ${J_m,m \ge 2}$ of the 3-state Mealy automata over an m-symbol alphabet such that the growth function of $J_m$ has the intermediate growth order $[n ^{{\log n}/{2 \log m}} ]$. For each automaton $J_m$ we describe the automaton transformation monoid $S_{J_m}$, defined by it, provide generating series for the growth functions, and consider primary properties of $S_{J_m}$ and $J_m$.38 pages, 5 Postscript figuresAlgebraic GeometryCombinatorics20M35; 68Q70On the 3-state Mealy Automata over an m-symbol Alphabet of Growth Order [ n ^{{\log n}/{2 \log m}} ]text