Benson's algorithm (Go)
In the game Go, Benson's algorithm (named after David Benson) can be used to determine the stones which are safe from capture no matter how many turns in a row the opposing player gets, i.e. unconditionally alive.[1]
Algorithm
Without loss of generality, we describe Benson's algorithm for the Black player.
Let X be the set of all Black chains and R to be the set of all Black-enclosed regions of X. Then Benson's algorithm requires iteratively applying the following two steps until neither is able to remove any more chains or regions:
- Remove from X all Black chains with less than two vital Black-enclosed regions in R.
- Remove from R all Black-enclosed regions with a surrounding stone in a chain not in X.
The final set X is the set of all unconditionally alive Black chains.[2]
References
- ^ Tapani Raiko (May 5, 2005). "Benson's algorithm". Retrieved March 21, 2012.
- ^ "Sensei's Library: Benson's Definition of Unconditional Life". Retrieved March 21, 2012.
- David B. Benson (1976). Information Sciences. 10 (2). Elsevier: 17–29 http://webdocs.cs.ualberta.ca/~games/go/seminar/2002/020717/benson.pdf. Retrieved March 21, 2012.
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