# Shortest paths in the Tower of Hanoi graph and finite automata

@article{Romik2006ShortestPI, title={Shortest paths in the Tower of Hanoi graph and finite automata}, author={Dan Romik}, journal={SIAM J. Discret. Math.}, year={2006}, volume={20}, pages={610-622} }

We present efficient algorithms for constructing a shortest path between two configurations in the Tower of Hanoi graph and for computing the length of the shortest path. The key element is a finite-state machine which decides, after examining on the average only a small number of the largest discs (asymptotically, $\frac{63}{38} \approx 1.66$), whether the largest disc will be moved once or twice. This solves a problem raised by Andreas Hinz and results in a better understanding of how the…

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### Email: romik@stat.berkeley

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