Re: On Game Space Size

[Henrik Rydberg <rydberg@xxxxxxxxxxxxxx>]

Robert Jasiek wrote:
>Proposition:
>If a position can be legally reached, then it can be reached by a 
>move-sequence without any removal.
...
>What about no pass rules?

A special case with a simple proof of the same kind:

Prop:

  Every state with N white stones and N or N+1 black
  stones can be reached without pass.

Proof:

  Noting that each stone in P (the target state) has at
  least one liberty, it follows by letting black play
  any of the occupied positions, followed by white, up
  til all positions are occupied. Since black starts the
  game, the sequence is always +1,0,+1,0,... Hence the
  note about N and N+1.

Now what if white has one more stone than black?

Henrik

-- 
Henrik Rydberg (http://fy.chalmers.se/~rydberg),
Department of Applied Physics, Chalmers University of Technology.