On composite and non-monotonic growth functions of Mealy automata

TL;DR

This paper introduces the concept of composite growth functions in Mealy automata, illustrating their properties with examples of non-monotonic and monotonic growth, and explores their interrelations.

Contribution

It defines and exemplifies composite growth functions in Mealy automata, highlighting their properties and the relationship between composite and non-monotonic growth.

Findings

Examples of Mealy automata with polynomial non-monotonic growth

Examples with intermediate and exponential monotonic growth

Formulation of questions on the relation between composite and non-monotonic growth

Abstract

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 automata that have composite non-monotonic growth functions of the polynomial growth order. There are described examples of Mealy automata that have composite monotonic growth functions of intermediate and exponential growth. The questions concerning the interrelation between the notions ``composite'' and ``non-monotonic'' of a Mealy automaton growth function are formulated.