Shortest paths in the tower of Hanoi graph and finite automata

SIAM Journal on Discrete Mathematics

Volumn 20, Issue 3, 2006, Pages 610-622

  Romik, Dan ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Finite automata; Sierpi ski gasket; Tower of Hanoi

Indexed keywords

ALGORITHMS; COMPUTATION THEORY; FINITE AUTOMATA; PROBLEM SOLVING; RANDOM PROCESSES;

RANDOM POINTS; TOWER OF HANOI;

GRAPH THEORY;

EID: 34547889538     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/050628660     Document Type: Article

References (13)

1. C. BANDT AND T. KUSCHEL, Self-similar sets VIII. Average interior distance in some fractals, Measure Theory (Oberwolfach, 1990), Rend. Circ. Mat. Palermo (2) Suppl., 28 (1992), pp. 307-317.
2. T. CHAN, A statistical analysis of the Towers of Hanoi problem, Internat. J. Comput. Math., 28 (1988), pp. 543-623.
3. M. C. ER, An analysis of the generalized Towers of Hanoi problem, BIT, 23 (1983), pp. 429-435.
4. R. L. GRAHAM, D. E. KNUTH, AND O. PATASHNIK, Concrete Mathematics, 2nd ed., Addison-Wesley, Reading, MA, 1994.
5. A. HINZ, The Tower of Hanoi, Enseign. Math., 35 (1989), pp. 289-321.
6. A. HINZ, Shortest paths between regular states of the Tower of Hanoi, Inform. Sci., 63 (1992), pp. 173-181.
7. A. HINZ, The Tower of Hanoi, in Algebras and Combinatorics (ICAC'97, Hong Kong), Springer, Singapore, 1999, pp. 277-289.
8. A. HINZ, S. KLAVZAR, U. MILUTINOVIC, D. PARISSE, AND C PETR, Metric properties of the Tower of Hanoi graphs and Stern's diatomic sequence, European J. Combin., 26 (2005), pp. 693-708.
9. A. HINZ AND A. SCHIEF, The average distance on the Sierpiński gasket, Probab. Theory Related Fields, 87 (1990), pp. 129-138.
10. S. KLAVZAR AND U. MILUTINOVIC, Graphs S(n, k) and a variant of the Tower of Hanoi problem, Czechoslovak Math. J., 47 (1997), pp. 95-104.
11. S. KLAVZAR, U. MILUTINOVIC, AND C PETR, On the Frame-Stewart algorithm for the multi-peg Tower of Hanoi problem, Discrete Appl. Math., 120 (2002), pp. 141-157.
12. I. STEWART, Le lion, le lama et la laitue, Pour la Science, 142 (1989), pp. 102-107.
13. P. K. STOCKMEYER, The Tower of Hanoi: A Historical Survey and Bibliography, version 0.2, preprint, 2001. Available online from http://www.cs.wm.edu/~pkstoc/h_papers.html.