Solving Box-Pushing Games via Model Checking with Optimizations

Box-pushing games are a challenging problem for both man and machine since it is not easy to find out a minimal solution for the games. This paper describes a formal framework for solving the games via symbolic model checking techniques. Since our method is automatic and sound, it gives a minimal solution if model checking succeeds. However, this framework is not complete so that it fails to find an answer in case the state explosion problem occurs. Push-Push chosen as a case game consists of 50 games. 43 games are solved with NuSMV but 7 failed due to the state explosion problem. Thus we devise several optimization techniques for the games to mitigate the state explosion problem such as abstraction, relay model checking, and efficient counterexample generations. As a result, we solve all games with minimal solution.

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