CoDE Publications CoDE Publications
IRIDIA Publications IRIDIA Publications
SMG Publications
WIT Publications
WIT Publications
SMG Publications
Home People Research Activities Publications Teaching Resources
By Class By Topic By Year
By Class By Topic By Year
login
S. Colette, J.-F. Raskin, and F. Servais. On the Symbolic Computation of the Hardest Configurations of the Rush Hour Game. In Proceedings of the 5th International Conference on Computers and Games, number 4630 in Lecture Notes in Computer Science, pages 220-233. Springer-Verlag, 2006.
© Springer-Verlag 2006

Abstract

RUSH HOUR is a sliding block game where blocks represent cars stuck in a traffic jam on a 6 x 6 board. The goal of the game is to allow one of the cars (the target car) to exit this traffic jam by moving the other cars out of its way. In this paper, we study the problem of finding difficult initial configurations for this game. An initial configuration is difficult if the number of car moves necessary to exit the target car is high. To solve the problem, we model the game in propositional logic and we apply symbolic model-checking techniques to study the huge graph of configurations that underlies the game. On the positive side, we show that this huge graph (containing 3.6 x 1010 vertices) can be completely analyzed using symbolic model-checking techniques with reasonable computing resources. We have classified every possible initial configuration of the game according to the length of its shortest solution. On the negative side, we prove a general theorem that shows some limits of symbolic model-checking methods for board games. This result explains why some natural modeling of board games leads to the explosion of the size of symbolic data-structures.


Updated: 2017-03-27