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:[EMAIL PROTECTED]] > Sent: Tuesday, November 26, 2002 12:29 PM > To: Ben Goertzel; [EMAIL PROTECTED] > 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" <[EMAIL PROTECTED]> > To: "Stephen Paul King" <[EMAIL PROTECTED]>; > <[EMAIL PROTECTED]> > 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:[EMAIL PROTECTED]] > > > Sent: Tuesday, November 26, 2002 9:25 AM > > > To: [EMAIL PROTECTED] > > > 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 > > > > > > > > > > > >
