Le Mercredi 31 Mai 2006 00:21, Hal Finney a écrit :
> The dovetailer I know does not seem relevant to this discussion about
> functions.  It generates programs, not functions.  For example, it
> generates all 1 bit programs and runs each for one cycle; then generates
> all 2 bit programs and runs each for 2 cycles; then generates all 3
> bit programs and runs each for 3 cycles; and so on indefinitely.  (This
> assumes that the 3 bit programs include all 2- and 1-bit programs, etc.)
> In this way all programs get run with an arbitrary number of cycles.

In fact it is relevant because of this :
- Bruno showed us that it is not possible to write a program that will list 
sequentially all growing functions.
- But the dovetailer will not do it too, but what it will do instead is 
generate all program that list "all" growing functions.

So it will first generate the programme that create the first sequence and 
also the pogram that create the sequence composed of diagonalisation of the 
first and so on... it can because program are countable because they are 
mapped to N. So the dovetailer will not list all the growing function but 
will generate (and execute in dovetailing) the infinite sequence of programs 
that generate all of them.

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