AND/OR tree search has been a fundamental topic in Artificial Intelligence, because many tasks can be decomposed into subtasks, such that either all (AND) or one (OR) of them must be solved. Recent AND/OR tree search algorithms have become powerful, especially by using the notion of proof and disproof numbers. However, there are limitations of these algorithms if the search space involves repetitions. Repetitions cause a problem of efficiency versus correctness. Some approaches incorrectly deal with repetitions to preserve search efficiency. As a result, they occasionally return incorrect solutions. Other approaches compromise efficiency to guarantee correctness. However, they are not efficient enough to become satisfactory choices of practitioners.; This thesis presents effective and correct methods for AND/OR tree search with repetitions. The one-eye problem in the game of Go, tsume-Go (life and death problem), and checkers are used as application domains to explore the new techniques.; The thesis contains four research contributions. First of all, a solution to the Graph History Interaction (GHI) problem, which may cause a solver to return the incorrect outcome because of repetitions, is presented. Theoretical and empirical results show that the GHI solution is general, correct, and efficient. Secondly, a performance problem is presented when the depth-first proof number (df-pn) search algorithm, which is an effective algorithm using proof and disproof numbers, is adapted to domains involving repetitions. A solution to the problem is given and dramatical improvements over df-pn are empirically achieved. Thirdly, on top of these solutions, domain dependent enhancements are added to the programs that solve the one-eye and tsume-Go problems. These techniques are very promising, and contribute to surpass the performance of the best existing tsume-Go solver. Finally, a divide and conquer approach that can reduce the search space is presented. This approach further improves the performance of the one-eye solver.
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