Automata theory is one of the most mathematical areas of computerscience. Two of the important uses of automata are:

1. to assist in the study and categorization of formal (computer) languages, and
2. to specify system behavior standards for implementable discrete systems.

One of the simplest types of automaton is the deterministic finiteautomaton (DFA) — the type used to recognize "regular" languages.Interestingly enough, the classical DFA is

• not deterministic,
• not finite, and
• not an automaton.

The details of this paradoxical contention will be explored usingconcepts of state-system specification.