Am 04.01.2011 23:48, schrieb Darren New:
> clipka wrote:
>> And that's no problem, because CA are allowed to have that /by
>> definition/.
>
> That right there is what I'm asking about. I've never seen a definition
> that allows for a CA to have an infinite initialization other than to a
> default state. Do you have a citation to a definition that describes
> this? I am having trouble coming up with a trivial way to define what
> would be the allowable initialization and what would be the disallowed
> initialization without making reference to something outside the realm
> of CAs. Perhaps if you can describe its state based on a RE function of
> its index or something?

"An initial state (time t=0) is selected by assigning a state for each 
cell."

(Wikipedia)

Isn't that plain enough? You assign a state for /each/ cell. CA's don't 
seem to make any limitations on this.

Just like you "create" a TM [tape] to be initially empty except for a 
limited section, you "create" a CA with an explicit initial state for 
/each/ cell. How you pick that state per cell is purely a CA design 
decision, and it doesn't matter whether you fetch that state out of thin 
air already providing (part of) your solution. Just name /any/ rule for 
that pattern - I guess the only limitation is that if you define the 
initial state at time t=0 as a function of any states at time t>0 you 
have a CA with oracle - and in fact may find yourself running straight 
into a paradoxon.

Post a reply to this message