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

Yodaiken, Victor

English

arXiv

Specifications of complex, large scale, computer software and hardware
systems can be radically simplified by using simple maps from input sequences
to output values. These "state machine maps" provide an alternative
representation of classical Moore type state machines. Composition of state
machine maps corresponds to state machine products and can be used to specify
essentially any type of interconnection as well as parallel and distributed
computation. State machine maps can also specify abstract properties of systems
and are significantly more concise and scalable than traditional
representations of automata. Examples included here include specifications of
producer/consumer software, network distributed consensus, real-time digital
circuits, and operating system scheduling. The motivation for this work comes
from experience designing and developing operating systems and real-time
software where weak methods for understanding and exploring designs is a well
known handicap. The methods introduced here are based on ordinary discrete
mathematics, primitive recursive functions and deterministic state machines and
are intended, initially, to aid the intuition and understanding of the system
developers. Staying strictly within the boundaries of classical deterministic
state machines anchors the methods to the algebraic structures of automata and
semigroups, obviates any need for axiomatic deduction systems, "formal
methods", or extensions to the model, and makes the specifications more
faithful to engineering practice. While state machine maps are obvious
representations of state machines, the techniques introduced here for defining
and composing them are novel. To illustrate applications, the paper includes a
fairly detailed specification and verification of the well-known "Paxos"
distributed consensus algorithm plus a number of simpler examples including a
digital PID controller

Practical State Machines for Computer Software and Engineering

Abstract

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