RE: The class of Boolean Algebras are a subset of the class of Turing Machines?

From: Ben Goertzel <ben.domain.name.hidden>
Date: Tue, 26 Nov 2002 12:49:04 -0500

The statement "Boolean Algebras are a subset of the class of Turing
Machines" doesn't seem quite right to me, I guess there's some kind of
logical typing involved there. A Turing machine is a kind of machine
[albeit mathematically modeled], whereas a boolean algebra is an algebra.

Boolean algebra is a mathematical framework that is sufficient to
model/design the internals of Turing machines...

In a conceptual sense, they're "equivalent" ...

-- Ben

> -----Original Message-----
> From: Stephen Paul King [mailto:stephenk1.domain.name.hidden]
> Sent: Tuesday, November 26, 2002 12:29 PM
> To: Ben Goertzel; everything-list.domain.name.hidden
> Subject: The class of Boolean Algebras are a subset of the class of
> Turing Machines?
>
>
> Dear Ben,
>
> So you are writing that the class of Boolean Algebras are a subset of
> the class of Turing Machines?
>
> Kindest regards,
>
> Stephen
>
> ----- Original Message -----
> From: "Ben Goertzel" <ben.domain.name.hidden>
> To: "Stephen Paul King" <stephenk1.domain.name.hidden>;
> <everything-list.domain.name.hidden>
> Sent: Tuesday, November 26, 2002 9:58 AM
> Subject: RE: turing machines = boolean algebras ?
>
>
> >
> > Essentially, you can consider a classic Turing machine to consist of a
> > data/input/output tape, and a program consisting of
> >
> > -- elementary tape operations
> > -- boolean operations
> >
> > I.e. a Turing machine program is a tape plus a program expressed in a
> > Boolean algebra that includes some tape-control primitives.
> >
> > -- Ben G
> >
> >
> > > -----Original Message-----
> > > From: Stephen Paul King [mailto:stephenk1.domain.name.hidden]
> > > Sent: Tuesday, November 26, 2002 9:25 AM
> > > To: everything-list.domain.name.hidden
> > > Subject: Re: turing machines = boolean algebras ?
> > >
> > >
> > > Dear Ben and Bruno,
> > >
> > > Your discussions are fascinating! I have one related and
> pehaps even
> > > trivial question: What is the relationship between the class of Turing
> > > Machines and the class of Boolean Algebras? Is one a subset of the
> other?
> > >
> > > Kindest regards,
> > >
> > > Stephen
> > >
> > >
> >
> >
>
>
Received on Tue Nov 26 2002 - 12:48:38 PST