Example illustrating the inversion rule

To provide another example, consider figure 21, where black must kill white b. The solution is to play black a, and as Anders Kierulf writes about this problem at http://www.smartgo.com (under Computer Go, Challenging Problems):

"How does a program know that the move at 'a' needs to be generated? At a top level, that is hard to do, unless you always include way too many moves. However, deeper in the search, it's very simple to generate that move (…). Is there an efficient way to propagate specific moves found deep in a search back to positions where the same move might be relevant earlier in the search? How do you decide that a move generated later might be valuable earlier?"

     
 
Fig. 21. Black to kill b   Fig. 22. Relevancy-zone for black

This problem (originating from problem 1 on page 61 in Tesuji by James Davies) can be easily solved in a l3-search, and the black l3-move at a is generated during search, since a failing la2-search yields the R*-zone depicted in figure 22.

The inversion rule finds that the white stone c in figure 22 is a 2-surrounding block, and since the white stone c has two quasi-liberties only (and hence q < nm + 3 = 2 – 2 + 3 = 3), these quasi-liberties are added to the R*-zone. Therefore, the killing l3-move a is generated by means of a relatively cheap l2-search, so the question Anders Kierulf poses seems to be answerable in the context of the l-search methodology.