ICGA Journal: The Journal of the Computer Games Community

Gradual Abstract Proof Search (GAPS) is a new 2-player search technique. It has been used to prove that 11×11 Phutball is a win for the first player in 25 plies or fewer, and that 6×6 Atari-Go with a crosscut in the centre is a win for the first player in 15 plies or fewer. In the paper, I give domain-dependent optimizations for the two games. Moreover, I describe theoretical and experimental comparisons with other related algorithms.

We introduce a variant of α-β search in which each node is associated with two depths rather than one. The purpose of α-β search is to find strategics for each player that together establish a value for the root position. A max strategy establishes a lower bound and the min strategy establishes an upper bound. It has long been observed that forced moves should be searched more deeply. Here we make the observation that in the max strategy we are only concerned with the forcedness of max moves and in the min strategy we are only concerned with the forcedness of min moves. This leads to two measures of depth — one for each strategy — and to a two-depth variant of α-β called ABC search. The two-depth approach can be formally derived from conspiracy theory and the structure of the ABC procedure is justified by two theorems relating ABC search and conspiracy numbers.

Parallel search programs use traditional alpha-beta tree searching, which includes the concept of transposition/refutation tables. Storing these entries in parallel can result in corrupt data that causes significant problems to the search. To prevent this, the common solution uses an atomic lock/unlock to implement a critical section that avoids the problem, but this incurs a significant performance penalty on many architectures. The paper describes a new approach that completely eliminates the need for any synchronization through locks, while still avoiding the problem of retrieving and using corrupted data.