Le 21-juin-06, à 11:19, Russell Standish a écrit :

>
> On Thu, Jun 22, 2006 at 10:29:30PM -0700, George Levy wrote:
>> In Bruno's calculus what are the invariances? (Comment on Tom 
>> Caylor's post)
>
> The main one relates to universal computation. For example, the coding
> theorem states that complexity measures will differ by at most a
> constant, regardless of which UTM you use.


Indeed. And then theoretical computer science is full of quite 
fundamental fixed point theorems, which provides invariants for the 
(total or partial) computable transformations. Eventually (who knows?) 
I will show how diagonalization provides such invariants. For example, 
when you apply any program to a universal sequence of programs (like 
those computing the Fi), there is always a program which behavior (= 
input-output) remains unchanged. This will be a key to introduce the 
notion of self-reference for machines.

Bruno

http://iridia.ulb.ac.be/~marchal/


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