Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Algorithms and Data Structures in VLSI Design
Algorithms and Data Structures in VLSI Design
Rush Hour is PSAPCE-complete, or "Why you should generously tip parking lot attendants"
Theoretical Computer Science
NuSMV 2: An OpenSource Tool for Symbolic Model Checking
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Theoretical Computer Science - Game theory meets theoretical computer science
Spin model checker, the: primer and reference manual
Spin model checker, the: primer and reference manual
GP-rush: using genetic programming to evolve solvers for the rush hour puzzle
Proceedings of the 11th Annual conference on Genetic and evolutionary computation
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RUSH HOUR is a sliding blocks game where blocks represent cars stuck in a traffic jam on a 6 × 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 ċ 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. The result explains why some natural modeling of board games leads to the explosion of the size of symbolic data-structures.