Re: Cardinality of Set of Computable Numbers?

From: George Greene (greeneg_at_greeneg-cs.cs.unc.edu)
Date: 12/29/03 

Date: 29 Dec 2003 15:08:16 -0500

"Russell Easterly" <logiclab@comcast.net> writes:

 : "|-|erc" <trymyform@wwwadamskingdom.com> wrote in message
 : news:pM8Hb.399$ma.13105@nnrp1.ozemail.com.au...
 : > ----------------------------- <^> <(·¿·)>
 : <^> -----------------------------
 : >
 : > "Russell Easterly" <logiclab@comcast.net> wrote in >
 : >
 : > > Any number having this form can be produced by an RM.
 : > > Some examples of computable numbers:
 : > >
 : > > (0)
 : > > (1)
 : > > 11(0)
 : > > 01(110)
 : > >
 : > > The length of the initial string plus the length of the repeating string
 : > > must be less than or equal to the number of states of the RM that
 : > > produced the number.
 : > >
 : >
 : > I don't see this. Here is a simplified conceptual diagram of a Russell
 : Machine.
 : >
 : > s1 s2 s6
 : > 0 s5
 : > ---------------------
 : > 1 s3
 : > s4 s7
 : > s8
 : >
 : > There is one piece of information missing, which state s8 goes to.
 : > Add to this s8 -> s7
 : >
 : > This RM will output 0 0 1 1 0 0 1 1 1 1 1 1 1 1
 : > notation is 0 0 1 1 0 0 (1 1)
 : >
 : > If it can't halt then the states get reused.
 :
 : I assume that s1->s2->s3->s4->s5->s6->s7->s8->s8.
 : The ouput is 001100(1).

Then it DOES halt, DUMBASS. s8 *IS* a halt state.

Are you now going to retract your claim that RMs don't halt because
they don't have halt states?

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