- Contemporary messages sorted: [ by date ] [ by thread ] [ by subject ] [ by author ] [ by messages with attachments ]

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

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

Received on Tue Nov 26 2002 - 12:48:38 PST

*
This archive was generated by hypermail 2.3.0
: Fri Feb 16 2018 - 13:20:07 PST
*