[anewhnaccount]

It's not playing fast and loose at all - at least not with the precise mathematical definition (perhaps it is playing fast and loose with the "literal every-day" definition which might mean a state machine with few enough states to fit on a whiteboard). A push down automata is defined as having infinite stack and a Turing machine is defined as having infinite tape. A finite stack push down automata permits an equivalent (much larger) finite state machine. A finite tape Turing machine also permits an equivalent (much much larger) finite state machine.

Leslie Lamport makes the same observation on page 4 here: http://research.microsoft.com/en-us/um/people/lamport/pubs/s...

The comment I replied to was "My experience shows it is a state machine, but I have not see any formal study of it." - I was simply replying "of course it's a state machine".

Lots of situations in GUIs can be modelled as quite compact state machines - but it depends on the level you model it at. If you need to model the state of a text box then your state machine will grow very large since you need a new state for every possible input string. Given modelling simplifications where we abstract away some parts with large state spaces by collapsing states, there are very few pieces of software which don't benefit from being modelled with state machines.

Personally I would be a very frustrated programmer and if I had to program user interfaces with Turing machines since writing a transition table would feel awfully low level and since the Turing machine model doesn't have any facilities for user interaction I'm not sure any users would be terribly happy with the result (so I'm not quite sure what you're trying to say here).