Cover

Preface

Contents

Index

Glossary

Models

Rogues

A Formal Definition

Page 1

Why bother?

Sometimes you might wonder why we have to go and spoil a perfectly acceptable informal description of something like a finite state automaton with a formal mathematical definition that has Greek symbols in it and other things that seem to make it hard to understand.  There are actually good many good reasons for formalisms, and, sometimes a few bad ones.

Think of it this way.  Look at all of the material you had to digest just to get to this page.  If you wanted to review this material, or describe finite state automaton to someone else, would you want to wade through all of this stuff again?  No?  Didn't think so.  Instead, we would like to have a short, formal, mathematically precise definition of a finite state automaton now that we know intuitively what one is.  Think of the benefits:

Clarity

A formal definition is like a standard. If two people disagree on what constitutes a valid finite state automaton, the disagreement can be resolved by referring to the definition.  If one had to wade through all of the previous English prose to try to come to an agreement, both sides would have to hire a lawyer and take the case to the Supreme Court to decide what was intended by certain things written as informal descriptions.  (This is precisely why we have Supreme Courts---to try to resolve conflicting interpretations of a country's constitution.)

Conciseness

Formal mathematical notation has a reason, too.  It is concise.  For example, we might write x instead of one side of the rectangle.  So, those Greek symbols serve a purpose.  They stand for an object or quantity that would have a description too long to use in text every time it needed to be discussed.

Precision

Mathematical notation is precise.  It takes a while to learn, but once learned it saves a lot of time and makes descriptions much clearer.