[CST-2] T in C
Kevin Chan
kkfc2@cam.ac.uk
Tue, 5 Jun 2001 23:35:31 +0100
With the least fixed point you start with an empty set and add fixed points
you can prove until you can prove no more.
With max fixed point you take a set of all expressions and take out all the
ones that you can prove to NOT be a fixed point.
Obviously the world of expressions must be finite for this to be true.
The difference between the two is that the max fixed point has the
expressions that can't be proved to be either a fixed point or not a fixed
point.
A little hand wavey but I hope that makes sense =)
Kev
----- Original Message -----
From: "Adam Martin" <amsm2@cam.ac.uk>
To: <cst-2@srcf.ucam.org>
Sent: Tuesday, June 05, 2001 11:29 PM
Subject: Re: [CST-2] T in C
> So, in that case... (with N = intersection, because Outlook won't let me
> type alt-139 for the intersection symbol....)
>
> With the minimum fixed point being the N{ S c S' | f(S) c S } why is the
> chain:
>
> f(0) c f(f(0)) c f(f(f(0))) ....
>
> an approximation to the min. prefixed. point?
>
> Surely the chain above is U{ S c S' | S c f(S) } - i.e. the max postfixed
> point?
>
> Sorry - this one has long confused me, but I never got around to going
over
> it a second time in supervisions!
>
> Adam
>
> ----- Original Message -----
> From: "Shu Yan Chan" <syc22@cam.ac.uk>
> To: <cst-2@srcf.ucam.org>
> Sent: Tuesday, June 05, 2001 10:02 PM
> Subject: Re: [CST-2] T in C
>
>
> > > Could someone give me a concise definition of:
> >
> > I will give it a try:
> >
> >
> > x is a fixed point for a function f(x) if f(x) = x (or the sets are of
> > equal size)
> >
> > x is a pre fixed point for a function f(x) if f(x) is a subset of x
> > x is a post fixed point for a function f(x) if x is a subset of f(x)
> >
> >
> > > A fixed point?
> > >
> > > A least fixed point?
> > >
> > > A most fixed point?
> > >
> > >
> > > I always kind of understood what he was on about, but I found I
couldn't
> > > neatly define those terms without just rephrasing the equations for
them
> > as
> > > used in Tarski's theorem.
> > >
> > > Regards,
> > > Adam
> > >
> > >
> > >
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> >
> >
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>
>
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