You may wish to consider Hilbert's axiomization of mathematics postulate
in your considerations of represenatation of a "machine."
Jerry LR Chandler
Don Mikulecky wrote:
>
> Don Mikulecky replies:
>
> yes your notation for Cartesian Product is clearer
>
> you will note that all my sets in the definition I used from Arbib's
> category theory are FINITE. Clealy, continuous intervals must be dealt with
> differently. This is more an issue of representation than a new conclusion
> as I see it. Am I missing something?
> Don
>
> Ricardo Ribeiro Gudwin wrote:
>
> > Don Mikulecky wrote:
> >
> > > Don Mikulecky comments:
> > >
> > > I offer an abstract definition of a machine to serve as an aid in
> > > discussing the machine metaphor and its limitations. Let's see if we
> > > can agree or else come up with something better?
> >
> > > DEFINITION: SEQUENTIAL MACHINE: SM = ( Xo, Q, Delta, qo,Y,Beta)
> > >
> > > Where
> > > Xo is the set of inputs
> > > Q is the set of states
> > > Delta: (Q X Xo) maps to Q is the dynamics
> > > qo is in Q is the initial state
> > > Y is the set of outputs
> > > Beta is the output map
> >
> > Hi, Don !
> > WHAT IF ...
> > Xo is a continuous interval
> > Delta is continous for Xo (wouldn't it be better to say Delta : Q x X ->
> > Q ore Delta(q,x) instead Delta:(Q X Xo) to not mix X (cartesian product
> > with Xo (set) ?)
> > Y is a continous interval
> > Do we still have a machine ? Or how should it be called ?
> > (Let's stay with Q finite for a while, we can make Q continuous further
> > ...)