# Primitive Recursive Presentations of Automata and their Products

## TL;DR

This paper introduces a method for representing Moore automata using primitive recursive functions and defines their parallel composition through simultaneous recursion, offering a concise approach to complex state systems in computing.

## Contribution

It presents a novel primitive recursive framework for automata specification and composition, linking automata theory with recursive function techniques.

## Key findings

- Primitive recursive representations simplify automata modeling.
- Parallel composition is achieved via simultaneous primitive recursion.
- Connections to algebraic automata theory and Krohn-Rhodes theorem are discussed.

## Abstract

Methods for specifying Moore type state machines (transducers) abstractly via primitive recursive functions and for defining parallel composition via simultaneous primitive recursion are discussed. The method is mostly of interest as a concise and convenient way of working with the complex state systems found in computer programming and engineering, but a short section indicates connections to algebraic automata theory and the theorem of Krohn and Rhodes.