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From: Marchal <marchal.domain.name.hidden>

Date: Fri May 4 07:24:58 2001

Hal Finney wrote also:

*>This leads to three questions:
*

*>
*

*> - Would all UD programs correspond to the universal measure,
*

*>asymptotically?
*

Universal measure defined on what ? (Well this is an ongoing

important discussion ...)

I do think that, for constructive universal measure whatsoever,

you can build, by diagonalisation, pathological

UD such that they will make that universal mesure biased .

The mesure could depend on some "natural" universal dovetailer

loosing only against *initial* pathological UD.

Actually I am not quite sure about that.

The difficulty of this question is one of my motivation to ask the

machines from "inside" (despite that UDA forces us to take that

inside view and only that inside view into account. (This will

hopefully be clearer later ...)

*> - Is there a way to retain state for all the programs so that you don't
*

*>have to start over from the beginning? (Although Chaitin's way may
*

*>be simpler, and if it gives the same probability distribution then we
*

*>couldn't tell the difference).
*

The UD I send you in my preceding post (in this thread) does that.

Perhaps you have already noticed. It never do the same computation

twice. Precisely it never run two times the execution of the i-th

programs Pi (the UD memorises the needed continuations). Of course, it

computes infinitely often all programs, because for all i there is

necessarily a bigger j such that Pi and Pj computes the same

functions. But then this is necessary for all possible UDs.

*> - Is it necessary to use self-delimiting programs in order for the
*

*>notion of running all programs to be well defined, and recover the
*

*>universal distribution?
*

I don't think so. Of course LISP programs are self-delimiting, so my UD is

not a counter-exemple.

If you are using non self-delimiting programs the UD will dovetail on each

runnable initial segments of the programs.

And you will probably recover the universal distribution,

if this one makes sense!

Perhaps you cannot compute in this way Chaitin's OMEGA because you cannot

know a priori if the UD execute a "correct non halting program" or just

some code which does not belong to a program (which cannot be extended in

a program code), so that I am not sure you can define when you must

add the 1/2^{-k} ...

Bruno

Received on Fri May 04 2001 - 07:24:58 PDT

Date: Fri May 4 07:24:58 2001

Hal Finney wrote also:

Universal measure defined on what ? (Well this is an ongoing

important discussion ...)

I do think that, for constructive universal measure whatsoever,

you can build, by diagonalisation, pathological

UD such that they will make that universal mesure biased .

The mesure could depend on some "natural" universal dovetailer

loosing only against *initial* pathological UD.

Actually I am not quite sure about that.

The difficulty of this question is one of my motivation to ask the

machines from "inside" (despite that UDA forces us to take that

inside view and only that inside view into account. (This will

hopefully be clearer later ...)

The UD I send you in my preceding post (in this thread) does that.

Perhaps you have already noticed. It never do the same computation

twice. Precisely it never run two times the execution of the i-th

programs Pi (the UD memorises the needed continuations). Of course, it

computes infinitely often all programs, because for all i there is

necessarily a bigger j such that Pi and Pj computes the same

functions. But then this is necessary for all possible UDs.

I don't think so. Of course LISP programs are self-delimiting, so my UD is

not a counter-exemple.

If you are using non self-delimiting programs the UD will dovetail on each

runnable initial segments of the programs.

And you will probably recover the universal distribution,

if this one makes sense!

Perhaps you cannot compute in this way Chaitin's OMEGA because you cannot

know a priori if the UD execute a "correct non halting program" or just

some code which does not belong to a program (which cannot be extended in

a program code), so that I am not sure you can define when you must

add the 1/2^{-k} ...

Bruno

Received on Fri May 04 2001 - 07:24:58 PDT

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