30 citations · 38 across the 4 of their papers we have counts for
4 papers
On the 3-state Mealy Automata over an m-symbol Alphabet of Growth Order [ n ^{{\log n}/{2 \log m}} ]
Illya I. Reznykov, Vitaliy I. Sushchansky
We consider the sequence of the 3-state Mealy automata over an m-symbol alphabet such that the growth function of has the intermediate growth order $[n ^{{\lo…
On composite and non-monotonic growth functions of Mealy automata
Illya I. Reznykov
We introduce the notion of composite growth function and provide examples that illustrate the primary properties of these growth functions. There are provided examples of Mealy aut…
A Mealy machine with polynomial growth of irrational degree
Laurent Bartholdi, Illya I. Reznykov
We consider a very simple Mealy machine (three states over a two-symbol alphabet), and derive some properties of the semigroup it generates. In particular, this is an infinite, fin…
The smallest Mealy automaton of intermediate growth
Laurent Bartholdi, Illya I. Reznykov, Vitaly I. Sushchansky
In this paper we study the smallest Mealy automaton of intermediate growth, first considered by the last two authors. We describe the automatic transformation monoid it defines, gi…