computer-go: unconditional life with suicide allowed

[Francois Grieu <fgrieu@xxxxxxxxxxx>]

A remark on unconditional life with suicide allowed.

Benson's unconditional life algorithm [*] is described with
suicide prohibited (assuming only the opponent plays, and
with no prior game history preventing moves by the ko rules,
which I suppose hereafter).

Suicide changes the outcome of unconditional life:

  .O.OX.
  OOOOX.
  XXXOXX
  .X.X.O

[all X can be killed if O can suicide the bottom right stone]

I remark that unconditional life with suicide allowed
is actually simpler, and reducible to unconditional life with
suicide prohibited:

  For any starting position (after removal of strings of
  stones that do not reach empty),
  a stone is unconditionally alive with suicide allowed
  if, and only if,
  it is unconditionally alive with suicide prohibited in
  the position derived by removing all opponent stones.

The proof is easy, using that
- if suicide is allowed, the opponent can change
  the starting position to the derived position;
- even with suicide prohibited, the opponent can change
  the derived position to the starting position.


  François Grieu

[*] David B. Benson: Life in the game of Go.
In Information Sciences, 10:17-29, 1976.
<http://persoweb.francenet.fr/~fgrieu/benson.pdf>