The Tower of Hanoi and finite automata

Some of the algorithms for solving the Tower of Hanoi puzzle can be applied "with eyes closed" or "without memory". Here we survey the solution for the classical Tower of Hanoi that uses finite automata, as well as some variations on the original puzzle. In passing, we obtain a new result on morphisms generating the classical and the lazy Tower of Hanoi.

[1]  Jean-Paul Allouche,et al.  Note on the Cyclic Towers of Hanoi , 1994, Theor. Comput. Sci..

[2]  G. Rauzy,et al.  Suites algébriques, automates et substitutions , 1980 .

[3]  A. M. Hinz,et al.  Pascal's triangle and the tower of Hanoi , 1992 .

[4]  T. Shallice.  Specific impairments of planning. , 1982, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[5]  J. Shallit,et al.  Morphisms, Squarefree Strings, and the Tower of Hanoi Puzzle , 1994 .

[6]  Andrew G. Glen,et al.  APPL , 2001 .

[7]  N. J. A. Sloane,et al.  The On-Line Encyclopedia of Integer Sequences , 2003, Electron. J. Comb..

[8]  Sandi Klavzar,et al.  Combinatorics of topmost discs of multi-peg Tower of Hanoi problem , 2001, Ars Comb..

[9]  Jeffrey Shallit,et al.  Sur Des Points Fixes De Morphismes D'Un Monoïde Libre , 1989, RAIRO Theor. Informatics Appl..

[10]  J. Saint-Cyr,et al.  Procedural learning and neostriatal dysfunction in man. , 1988, Brain : a journal of neurology.

[11]  Amir Sapir,et al.  The Tower of Hanoi with Forbidden Moves , 2004, Comput. J..

[12]  Alfred J. van der Poorten,et al.  Automatic sequences. Theory, applications, generalizations , 2005, Math. Comput..

[13]  Sandi Klavzar,et al.  Metric properties of the Tower of Hanoi graphs and Stern's diatomic sequence , 2005, Eur. J. Comb..

[14]  H. Simon,et al.  The functional equivalence of problem solving skills , 1975, Cognitive Psychology.

[15]  Gilles Christol,et al.  Ensembles Presque Periodiques k-Reconnaissables , 1979, Theor. Comput. Sci..

[16]  A. M. Hinz,et al.  The average distance on the Sierpiński gasket , 1990 .

[17]  Jeffrey Shallit,et al.  Automatic Sequences: Theory, Applications, Generalizations , 2003 .

[18]  A. Salomaa.  On exponential growth in Lindenmayer systems , 1973 .

[19]  S. Klavžar,et al.  Hanoi graphs and some classical numbers , 2005 .

[20]  Jeffrey Shallit,et al.  The Ubiquitous Prouhet-Thue-Morse Sequence , 1998, SETA.

[21]  Jean-Paul Allouche,et al.  Restricted Towers of Hanoi and Morphisms , 2005, Developments in Language Theory.