Skip to main content Accessibility help

Decidability of the HD0L ultimate periodicity problem

  • Fabien Durand (a1)


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



Hide All
[1] Allouche, J.-P., Rampersad, N. and Shallit, J., Periodicity, repetitions, and orbits of an automatic sequence. Theoret. Comput. Sci. 410 (2009) 27952803.
[2] J.-P. Allouche and J.O. Shallit, Automatic Sequences, Theory, Applications, Generalizations. Cambridge University Press (2003).
[3] 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) 809839.
[4] Cassaigne, J. and Nicolas, F., Quelques propriétés des mots substitutifs. Bull. Belg. Math. Soc. Simon Stevin 10 (2003) 661676.
[5] A. Cerný and J. Gruska, Modular trellises. The Book of L, edited by G. Rozenberg and A. Salomaa. Springer-Verlag (1986) 45–61.
[6] 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.
[7] Durand, F., A characterization of substitutive sequences using return words. Discrete Math. 179 (1998) 89101.
[8] Durand, F., HD0L ω-equivalence and periodicity problems in the primitive case (To the memory of G. Rauzy). J. Unif. Distrib. Theory 7 (2012) 199215.
[9] Durand, F. and Rigo, M., Multidimensional extension of the Morse-Hedlund theorem. Eur. J. Comb. 34 (2013) 391409.
[10] Harju, T. and Linna, M., On the periodicity of morphisms on free monoids. RAIRO ITA 20 (1986) 4754.
[11] Honkala, J., A decision method for the recognizability of sets defined by number systems. RAIRO ITA 20 (1986) 395403.
[12] Honkala, J., Cancellation and periodicity properties of iterated morphisms. Theoret. Comput. Sci. 391 (2008) 6164.
[13] Honkala, J., On the simplification of infinite morphic words. Theoret. Comput. Sci. 410 (2009) 9971000.
[14] Honkala, J. and Rigo, M., Decidability questions related to abstract numeration systems. Discrete Math. 285 (2004) 329333.
[15] R.A. Horn and C.R. Johnson, Matrix analysis. Cambridge University Press (1990).
[16] Lecomte, P. and Rigo, M., Abstract numeration systems. In Combinatorics, automata and number theory, Cambridge Univ. Press. Encyclopedia Math. Appl. 135 (2010) 108162.
[17] 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.
[18] D. Lind and B. Marcus, An Introduction to Symbolic Dynamics and Coding. Cambridge University Press (1995).
[19] Maes, A. and Rigo, M., More on generalized automatic sequences. J. Autom. Lang. Comb. 7 (2002) 351376.
[20] I. Mitrofanov, A proof for the decidability of HD0L ultimate periodicity. arXiv:1110.4780 (2011).
[21] Muchnik, A., The definable criterion for definability in Presburger arithmetic and its applications. Theoret. Comput. Sci. 290 (2003) 14331444.
[22] Pansiot, J.-J., Hiérarchie et fermeture de certaines classes de tag-systèmes. Acta Informatica 20 (1983) 179196.
[23] 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.
[24] Pansiot, J.-J., Decidability of periodicity for infinite words. RAIRO ITA 20 (1986) 4346.
[25] Priebe, N., Towards a characterization of self-similar tilings in terms of derived Voronoĭ tessellations. Geom. Dedicata 79 (2000) 239265.
[26] Priebe, N. and Solomyak, B., Characterization of planar pseudo-self-similar tilings. Discrete Comput. Geom. 26 (2001) 289306.
[27] M. Queffélec, Substitution dynamical systems–spectral analysis. In Lect. Notes Math., Vol. 1294. Springer-Verlag (1987).
[28] O. Salon, Suites automatiques à multi-indices. In Séminaire de Théorie des Nombres de Bordeaux (1986-1987) 4.01–4.27.
[29] Salon, O., Suites automatiques à multi-indices et algébricité. C. R. Acad. Sci. Paris 305 (1987) 501504.


Related content

Powered by UNSILO

Decidability of the HD0L ultimate periodicity problem

  • Fabien Durand (a1)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.