Using games for benchmarking and representing the complete solution space using symbolic techniques

Games often are inherently multi-valued problems and their wide variety offers different graduations of complexity. Moreover a lot of games have a parameter, like board-size that allows to generate differently sized instances of the same problem. All this makes them perfectly suitable for benchmarking in the multi-valued domain. So far the lack of benchmarks in this area often was compensated by transferring problems from binary to multi-valued, but for several application domains this is not adequate. This paper focuses on three games, that we consider suitable for benchmarking. We show the differences in complexity of the games and compare two coding schemes for one of them. All three problems are modeled by symbolic techniques, namely decision diagrams, leading to a complete representation of the solution space. This representation finds several applications, e.g. in objectively analyzing the efficiency of different heuristics on a solution space or to speed up learning algorithms.