Here’s a graph of a simple state machine of somewhat under 512 states that models a dumb fifo queue. The initial state is “e” for empty. We can append 1,2 or 3 to this queue and can delete the first in. To simplify suppose the alphabet is {0,1,2,3} where 0 means “dequeue” and the others mean to enq the designated number. Enqueue to a full queue has no effect on state. Ok, the diagram is completely unreadable – but click on the PDF to the right. It’s still unreadable. This diagram, generated with ATT’s “dot” program could undoubtedly be improved, but it shows why state diagrams are just not making it as descriptions of complex systems – this system is far from complex.

q4statemachine

To see the structure hidden in this diagram we have to look at it through algebra and programs.