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A family of tag systems for paperfolding sequences

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STACS 95 (STACS 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 900))

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Abstract

If one folds in two parts a strip of paper several times on itself (all folds being parallel) one obtains after unfolding a sequence of “valley” and “ridge” folds. If one codes these folds over a two-letter alphabet, one obtains a paperfolding word associated to the sequence of folding instructions. A paperfolding sequence is an infinite paperfolding word.

This paper is devoted to the effective construction of 2-uniform tag systems which generate every paperfolding sequences associated to ultimately periodic sequences of (un)folding instructions.

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References

  1. S. I. Adian, The Burnside Problem and Identities in Groups, Springer-Verlag, 1979.

    Google Scholar 

  2. J.-P. Allouche, Automates finis en théorie des nombres, Expo. Math. 5, (1987) 239–266.

    Google Scholar 

  3. J.-P. Allouche, The number of factors in a paperfolding sequences, Bull. Austral. Math. Soc. 46 (1992) 23–32.

    Google Scholar 

  4. J.-P. Allouche, R. Bacher, Toeplitz sequences, paperfolding, towers of Hanoi and progression-free sequences of integers, Ens. Math. 38 (1992) 315–327.

    Google Scholar 

  5. J.-P. Allouche, M. Bousquet-Mélou, Canonical positions for the factors in the paper-folding sequences, (1993) to appear in Theor. Comp. Sci.

    Google Scholar 

  6. J. Berstel, Mots sans carrés et morphismes itérés, Discrete Math. 29 (1980) 235–244.

    Google Scholar 

  7. J. Berstel, Every iterated morphism yields a co-CFL, Inform. Proc. Lett. 22 (1986) 7–9.

    Google Scholar 

  8. G. Christol, T. Kamae, M. Mendés-France, G. Rauzy, Suites algébriques, automates et substitutions, Bull. Soc. math. France 108 (1980) 401–419.

    Google Scholar 

  9. A. Cobham, Uniform Tag Sequences, Math. Systems Theory 6 (1972) 164–192.

    Google Scholar 

  10. K. Culik II, I. Fris, The decidability of the Equivalence Problem for DOL-Systems, Inform. Control 35 (1977) 20–39.

    Google Scholar 

  11. C. Davis, D. E. Knuth, Number representations and dragon curves, J. Recreational Math. t. 3 (1970) 66–81 and 133–149.

    Google Scholar 

  12. M. Dekking, M. Mendés-France, A. J. van der Poorten, Folds! Math. Intell. 4 (1983) n∘ 3:130–138, n∘ 4: 173–181 and 190–195.

    Google Scholar 

  13. A. Ehrenfeucht, G. Rozenberg, Elementary homomorphisms and a solution to the dol sequence equivalence problem, Theor. Comp. Sci. 7 (1978) 169–187.

    Google Scholar 

  14. M. Gardner, Mathematical games, Scientific American (1967) 216:118–125, 217:115.

    Google Scholar 

  15. M. Harrison, Introduction to formal language theory, Addison-Wesley, Read. Mass., 1978.

    Google Scholar 

  16. S. Istrail, On irreductible languages and nonrational numbers, Bull. Math. Soc. Sci. Math. R.S. Roumanie 21 (1977) 301–308.

    Google Scholar 

  17. J. Karhumäki, On the Equivalence Problem for Binary DOL Systems, Inform. Control 50 (1981) 276–284.

    Google Scholar 

  18. M. Lothaire, Combinatorics on words, Addison-Wesley, Reading, Mass., 1983.

    Google Scholar 

  19. M. Mendés-France, Principe de la symétrie pertubée, Séminaire de théorie des nombres Paris 1980, in Séminaire Delange-Pisot (1981) 77–98.

    Google Scholar 

  20. M. Mendés-France, J. Shallit, Wire Bending, J. Comb. Theory, Serie A 50 (1989) 1–23.

    Google Scholar 

  21. M. Mendés-France, A. J. van der Poorten, Arithmetic and analytic properties of paper sequences, Bull. Austral. Math. Soc. 24 (1981) 123–131.

    Google Scholar 

  22. M. Morse, Recurrent geodesies on a surface of negative curvature, Trans. Amer. Math. Soc. 22 (1921) 84–100.

    Google Scholar 

  23. M. Morse, G. A. Hedlund, Symbolic dynamics, Amer. J. Math. 60 (1938) 815–866.

    Google Scholar 

  24. M. Morse, G. A. Hedlund, Symbolic dynamics II-Sturmian trajectories, Amer. J. Math. 62 (1940) 1–42.

    Google Scholar 

  25. D. Razafy Andriamampianina, Le p-pliage de papier, Ann. fac. Sci. Toulouse Math. vol X n∘ 1 (1989) 401–414.

    Google Scholar 

  26. G. Rozenberg, A. Salomaa, The Mathematical Theory of L Systems, Acad. Press, 1980.

    Google Scholar 

  27. A. Salomaa, Formal languages, Academic Press, London, 1973.

    Google Scholar 

  28. M. P. Schützenberger, On a special class of recurrent events, Annals Math. Stat. 322 (1961) 1201–1213.

    Google Scholar 

  29. A. Thue, Über unendliche Zeichenreihen, Christiania Vid. Selsk. Skr. I. Mat.-Nat. Kl. 7, (1906) 1–22.

    Google Scholar 

  30. A. Thue, Über die gegenseitige Lage gleicher Teile gewisser Zeichenreihen, Vldensk. Skr. I. Mat.-Naturv. Kl. 1, Kristiania (1912) 1–67.

    Google Scholar 

  31. A. J. van der Poorten, J. Shallit, Folded continued fractions, J. Number Theory 40 (1992) 237–250.

    Google Scholar 

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Author information

Authors and Affiliations

  1. I.U.T. de Soissons, les Terrasses du Mail, 02880, Cuffies, France

    Christiane Bercoff

  2. LAMIFA, 33 rue Saint Leu, 80039, Amiens Cedex, France

    Christiane Bercoff

Authors
  1. Christiane Bercoff
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Ernst W. Mayr Claude Puech

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© 1995 Springer-Verlag Berlin Heidelberg

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Bercoff, C. (1995). A family of tag systems for paperfolding sequences. In: Mayr, E.W., Puech, C. (eds) STACS 95. STACS 1995. Lecture Notes in Computer Science, vol 900. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59042-0_82

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  • DOI: https://doi.org/10.1007/3-540-59042-0_82

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-59042-2

  • Online ISBN: 978-3-540-49175-0

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