Re: re:Entropy

From: Theorist (Alexey007_at_hotmail-dot-com.no-spam.invalid)
Date: 11/09/04 

Date: 9 Nov 2004 03:27:16 -0600

> Paul Chapmanwrote:
"Theorist" <Alexey007@hotmail-dot-com.no-spam.invalid> wrote in
message
> news:418fe4b6_1@Usenet.com...
> We can define a digit sequence without a pattern as one which
cannot
> be generated by a finite Turing machine.
>
> Let's enumerate all the Turing machines that produce sequences of
> digits.
>
How?

<snip>

Cheers, Paul[/quote:c289186c6c]

First you enumerate all the Turing machines using the Godel
numeration, then you single out those that produce digit sequences
(of course as the argument shows you can't do it effectively, but it
can be defined mathematically).

*-----------------------*
        Posted at:
  www.GroupSrv.com
*-----------------------*

Relevant Pages

  • Re: Turing completeness of the functional paradigm?
    ... beyond what is usual for constructive mathematics. ... We can enumerate ... do compute total functions N->N, ...
    (sci.logic)
  • Re: CERT C Programming Language Secure Coding Standard
    ... There is an enumerable set of exceptional conditions ... (More likely they meant that it is possible to enumerate all these ... all right to flout the rules if the exceptional circumstances ... The set of all possible Turing machines is ...
    (comp.lang.c)
  • Re: re:Entropy
    ... > We can define a digit sequence without a pattern as one which cannot ... > be generated by a finite Turing machine. ... > Let's enumerate all the Turing machines that produce sequences of ...
    (sci.math)