Re: On Game Space Size

[Robert Jasiek <jasiek@xxxxxxxxxxxxxxx>]

Andre Engels wrote:
> Lemma 3:
> Any position that can be legally reached (under no pass rules) under any
> ko rule, can be legally reached under situational superko.

Under no pass rules situational superko and natural situational
superko are equal.

> Proof:
> Look at a legal game under any ko rule that leads to the given position. We
> now transform this game into one that is legal under situational superko as
> follows:
> Take the first move in the game that would be legal under situational
> superko. Call this move b. It would be a move to a position which had
> already occured in the same game with the same player to move.

Typo: Replace the last "legal" by "illegal". Otherwise your proofs
are fine.

Applications to rules with passes are possible:

Proposition 5:
Any position that can be legally reached under some
ko rule(s), can be legally reached under natural situational superko.

Proof:
As for lemma 3, add "natural" where necessary.

Proposition 6:
Any position that can be legally reached under some
ko rule(s), can be legally reached under situational superko.

Proof:
As for lemma 3; after each removal of moves, if both the move to a
and the move after b are passes, then remove them as well.

Corollaries:
Corollary 4 can be adapted to propositions 5 and 6.

Question:
For no pass go, does a position exist that is legal under
situational superko and illegal under positional superko?
This is of some importance for corollary 4...

-- 
robert jasiek
http://www.snafu.de/~jasiek/korules.html