State machines for large scale computer software and systems

A method for specifying the behavior and architecture of discrete state systems such as digital electronic devices and software using deterministic state machines and automata products. The state machines are represented by sequence maps $f:A^*\to X$ where $f(s)=x$ indicates that the output of the system is $x$ in the state reached by following the sequence of events $s$ from the initial state. Examples provided include counters, networks, reliable message delivery, real-time analysis of gates and latches, and producer/consumer. Techniques for defining, parameterizing, characterizing abstract properties, and connecting sequence functions are developed. Sequence functions are shown to represent (possibly non-finite) Moore type state machines and general products of state machines. The method draws on state machine theory, automata products, and recursive functions and is ordinary working mathematics, not involving formal methods or any foundational or meta-mathematical techniques. Systems in which there are levels of components that may operate in parallel or concurrently are specified in terms of function composition

Practical State Machines for Computer Software and Engineering

This paper introduces methods for describing properties of possibly very large state machines in terms of solutions to recursive functions and applies those methods to computer systems