Title: The growth rates of automaton groups generated by reset automata,
Abstract: We give sufficient conditions for when groups generated by automata in a
class $\mathcal{C}$ of transducers, which contains the class of reset automata
transducers, have infinite order. As a consequence we also demonstrate that if
a group generated by an automata in $\mathcal{C}$ is infinite, then it contains
a free semigroup of rank at least 2. This gives a new proof, in the context of
groups generated by automaton in $\mathcal{C}$, of a result of Chou showing
that finitely generated elementary amenable groups either have polynomial
growth or contain a free semigroup of rank at least 2.
We also study what we call the `core growth rate' of elements of
$\mathcal{C}$. This turns out to be equivalent to the growth rate of certain
initial transducers. We give examples of transducers with exponential core
growth rate, and conjecture that all infinite order transducers in the class
$\mathcal{C}$ have exponential core growth rate.