You're both right in the examples of state machines.

I agree with Richard that a sequencer is a form of a state machine.

And Steve (or CMMan if you prefer) is correct too in describing another form of state machine.

First I'll point out that there is a duality around state machine diagram methods; a Moore and Mealey type. This will add to confusion when people compare their definitions.

The easy definition of a state machine is a method of organizing a process.

Commonly represented as Circles and interconnecting Arrows, tabular forms exist too; for those brave enough to decode the IrDA Specification you may realize that their endless text is merely a harder way of describing their state machine - not everyone agrees that a picture is worth a thousand words.

The idea of a STATE commonly represented by a circle with notes inside, is that it is a stable state that won't change until some condition (Richard is right that a valid condition can be a timing delay or merely an absolute jump, hence sequencers are valid).

Most people think of the circle states being mapped to one specific output state, though the duality case doesn't require this. The duality case assigns an output state to the arrow transition. This has certain advantages in some applicaions but we needed tie our brains in knots today. :)

State machines are sometimes contrasted to flow charts but they can be either more or less detailed depending upon the application.

State machines are used a lot in Operations Research as you'd expect since its involved in improving process efficiencies and in statistical modeling. I'll shut up on that or else I'll reveal some more time wasted in grad school. :)

aka J