Benson's Algorithm/ Discussion
term100?: Can Benson's algorithm be adapted for rulesets that allow suicide?
Robert Pauli: Yes, just restrict healthy regions additionally to be without interior.
term100?: But wouldn't that make the algorithm no longer both necessary and sufficient for proving unconditional life?
Robert Pauli:
- Sorry, I slipped (interior is not relative to the block). Replace it with:
Yes, just restrict healthy regions additionally to be without any intersection not adjacent to the block using them as such.
- Didn't prove it, but I strongly feel that this would make Benson's "safe" equivalent to his "unconditional alife" under with-suicide.
- Example
![[Diagram]](../../diagrams/16/574c3dfcdc6ed4ac444d5fd7374553ce.png)
Not "safe"
![[Diagram]](../../diagrams/4/d3a70f728d22ee6bed5e811d8d868b44.png)
"Safe"