Limits of Rush Hour Logic Complexity
<|reference_start|>Limits of Rush Hour Logic Complexity: Rush Hour Logic was introduced in [Flake&Baum99] as a model of computation inspired by the ``Rush Hour'' toy puzzle, in which cars can move horizontally or vertically within a parking lot. The authors show how the model supports polynomial space computation, using certain car configurations as building blocks to construct boolean circuits for a cpu and memory. They consider the use of cars of length 3 crucial to their construction, and conjecture that cars of size 2 only, which we'll call `Size 2 Rush Hour', do not support polynomial space computation. We settle this conjecture by showing that the required building blocks are constructible in Size 2 Rush Hour. Furthermore, we consider Unit Rush Hour, which was hitherto believed to be trivial, show its relation to maze puzzles, and provide empirical support for its hardness.<|reference_end|>
@article{tromp2005limits,
    title={Limits of Rush Hour Logic Complexity},
    author={John Tromp and Rudi Cilibrasi},
    journal={arXiv preprint arXiv:cs/0502068},
    year={2005},
    archivePrefix={arXiv},
    eprint={cs/0502068},
    primaryClass={cs.CC}
}