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

Abstract

We 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 figures

References in corpus (2)

• The smallest Mealy automaton of intermediate growth
• On composite and non-monotonic growth functions of Mealy automata