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Decidability of the HD0L ultimateperiodicity problem

Published online by Cambridge University Press:  25 April 2013

Fabien Durand
Fabien Durand*
Affiliation:
Université de Picardie Jules Verne, Laboratoire Amiénois de Mathématiques Fondamentales et Appliquées, CNRS-UMR 7352, 33 rue Saint Leu, 80039 Amiens Cedex 01, France. fabien.durand@u-picardie.fr
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Abstract

In this paper we prove the decidability of the HD0L ultimate periodicity problem.

Keywords

HD0L – periodicity – decidability – return words
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 47 , Issue 2 , April 2013 , pp. 201 - 214
Copyright
© EDP Sciences 2013

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References

Allouche, J.-P., Rampersad, N. and Shallit, J., Periodicity, repetitions, and orbits of an automatic sequence. Theoret. Comput. Sci. 410 (2009) 2795–2803. Google Scholar
J.-P. Allouche and J.O. Shallit, Automatic Sequences, Theory, Applications, Generalizations. Cambridge University Press (2003).
Bell, J.P., Charlier, E., Fraenkel, A.S. and Rigo, M., A decision problem for ultimately periodic sets in non-standard numeration systems. Internat. J. Algebra Comput. 9 (2009) 809–839. Google Scholar
Cassaigne, J. and Nicolas, F., Quelques propriétés des mots substitutifs. Bull. Belg. Math. Soc. Simon Stevin 10 (2003) 661–676. Google Scholar
A. Cerný and J. Gruska, Modular trellises. The Book of L, edited by G. Rozenberg and A. Salomaa. Springer-Verlag (1986) 45–61.
A. Cobham, On the Hartmanis-Stearns problem for a class of tag machines. In IEEE Conference Record of 1968 Ninth Annual Symposium on Switching and Automata Theory. Also appeared as IBM Research Technical Report RC-2178, August 23 (1968) 51–60.
Durand, F., A characterization of substitutive sequences using return words. Discrete Math. 179 (1998) 89–101. Google Scholar
Durand, F., HD0L ω-equivalence and periodicity problems in the primitive case (To the memory of G. Rauzy). J. Unif. Distrib. Theory 7 (2012) 199–215. Google Scholar
Durand, F. and Rigo, M., Multidimensional extension of the Morse-Hedlund theorem. Eur. J. Comb. 34 (2013) 391–409. Google Scholar
Harju, T. and Linna, M., On the periodicity of morphisms on free monoids. RAIRO ITA 20 (1986) 47–54. Google Scholar
Honkala, J., A decision method for the recognizability of sets defined by number systems. RAIRO ITA 20 (1986) 395–403. Google Scholar
Honkala, J., Cancellation and periodicity properties of iterated morphisms. Theoret. Comput. Sci. 391 (2008) 61–64. Google Scholar
Honkala, J., On the simplification of infinite morphic words. Theoret. Comput. Sci. 410 (2009) 997–1000. Google Scholar
Honkala, J. and Rigo, M., Decidability questions related to abstract numeration systems. Discrete Math. 285 (2004) 329–333. Google Scholar
R.A. Horn and C.R. Johnson, Matrix analysis. Cambridge University Press (1990).
Lecomte, P. and Rigo, M., Abstract numeration systems. In Combinatorics, automata and number theory, Cambridge Univ. Press. Encyclopedia Math. Appl. 135 (2010) 108–162. Google Scholar
J. Leroux, A polynomial time presburger criterion and synthesis for number decision diagrams. In 20th IEEE Symposium on Logic In Computer Science (LICS 2005), IEEE Comput. Soc. (2005) 147–156.
D. Lind and B. Marcus, An Introduction to Symbolic Dynamics and Coding. Cambridge University Press (1995).
Maes, A. and Rigo, M., More on generalized automatic sequences. J. Autom. Lang. Comb. 7 (2002) 351–376. Google Scholar
I. Mitrofanov, A proof for the decidability of HD0L ultimate periodicity. arXiv:1110.4780 (2011).
Muchnik, A., The definable criterion for definability in Presburger arithmetic and its applications. Theoret. Comput. Sci. 290 (2003) 1433–1444. Google Scholar
Pansiot, J.-J., Hiérarchie et fermeture de certaines classes de tag-systèmes. Acta Informatica 20 (1983) 179–196. Google Scholar
J.-J. Pansiot, Complexité des facteurs des mots infinis engendrés par morphismes itérés. In ICALP84, Lect. Notes Comput. Sci. Vol. 172, edited by J. Paredaens. Springer-Verlag (1984) 380–389.
Pansiot, J.-J., Decidability of periodicity for infinite words. RAIRO ITA 20 (1986) 43–46. Google Scholar
Priebe, N., Towards a characterization of self-similar tilings in terms of derived Voronoĭ tessellations. Geom. Dedicata 79 (2000) 239–265. Google Scholar
Priebe, N. and Solomyak, B., Characterization of planar pseudo-self-similar tilings. Discrete Comput. Geom. 26 (2001) 289–306. Google Scholar
M. Queffélec, Substitution dynamical systems–spectral analysis. In Lect. Notes Math., Vol. 1294. Springer-Verlag (1987).
O. Salon, Suites automatiques à multi-indices. In Séminaire de Théorie des Nombres de Bordeaux (1986-1987) 4.01–4.27.
Salon, O., Suites automatiques à multi-indices et algébricité. C. R. Acad. Sci. Paris 305 (1987) 501–504. Google Scholar