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
> ...)
>
> --
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