Abstract
PDF (258 K)
E-mail Article
Add to my Quick Links
Cited By in Scopus (0)
doi:10.1016/j.entcs.2008.03.010 
Copyright © 2008 Elsevier B.V. All rights reserved.
Effective Symbolic Dynamics
Douglas Cenzer1, a, 
, S. Ali Dashtib, and Jonathan L.F. Kingb,
Available online 20 March 2008.
Abstract
We investigate computable subshifts and the connection with effective symbolic dynamics. It is shown that a decidable class P is a subshift if and only if there is a computable function F mapping
to
such that P is the set of itineraries of elements of
. A
subshift is constructed which has no computable element. We also consider the symbolic dynamics of maps on the unit interval.
References
M. Braverman and M. Yampolski, Non-computable Julia sets, J. Amer. Math. Soc. 19 (2006), pp. 551–578. View Record in Scopus | Cited By in Scopus (8)
D. Cenzer, Effective dynamics. In: J. Crossley, J. Remmel, R. Shore and M. Sweedler, Editors, Logical Methods in honor of Anil Nerode's Sixtieth Birthday, Birkhauser (1993), pp. 162–177.
D. Cenzer and J.B. Remmel, 
classes in mathematics. In: Y. Ersov, S. Goncharov, A. Nerode and J.B. Remmel, Editors, Recursive Mathematics, Studies in Logic and Found. Math. 138, North-Holland (1998), pp. 623–821. Abstract | 
PDF (9297 K)
PDF (9297 K)
Cenzer, D. and J.B. Remmel, “Effectively closed sets”, Association for Symbolic Logic Lecture Notes, to appear.
P. Collet and J.P. Eckmann, Iterated Maps On The Interval As Dynamical Systems, Birkhuser (1980).
Delvenne, J.-C. “Dynamics, Information and Computation”, Ph. D. thesis, Universite Catholique De Louvain (2005).
J.-C. Delvenne, P. Kurka and V. Blondel, Decidability and Universality in Symbolic Dynamical Systems, Fund. Informaticae 74 (2006), pp. 463–490. View Record in Scopus | Cited By in Scopus (3)
A. Grzegorczyk, On the definitions of computable real continuous functions, Fund. Math. 44 (1957), pp. 61–71.
W. Huang and A. Nerode, Applications of pure recursion theory to recursive analysis, Acta Sinica 28 (1985), pp. 625–636.
K. Ko, Complexity Theory of Real Functions, Birkhauser (1991).
K. Ko, On the computability of fractal dimensions and Julia sets, Ann. Pure Appl. Logic 93 (1998), pp. 195–216. Abstract | PDF (1502 K)
| View Record in Scopus | Cited By in Scopus (7)
PDF (1502 K)
| View Record in Scopus | Cited By in Scopus (7)D. LaCombe, Extension de la notion de fonction recursive aux d'une ou plusieurs variables reelles, Comptes Rendus Acad. Sci. Paris 241 (1955), pp. 2478–2480.
D. Lind and B. Marcus, An Introduction to Symbolic Dynamics and Coding, Cambridge University Press (1995).
N. Metropolis, M.L. Stein and P.R. Stein, On Finite Limit Sets for Transformation of the Unit Interval, Journal of Combinatorial Theory (A) 15 (1973), pp. 25–44. Abstract | Article | PDF (985 K)
| View Record in Scopus | Cited By in Scopus (135)
PDF (985 K)
| View Record in Scopus | Cited By in Scopus (135)R. Rettinger and K. Weihrauch, The computational complexity of some Julia sets. In: M.X. Goemans, Editor, Proc. 35th ACM Symposium on Theory of Computing (San Diego, June 2003), ACM Press, New York (2003), pp. 177–185.
K. Weihrauch, Computable Analysis, Springer (2000).
H. Xie, Grammatical Complexity And One-Dimensional Dynamical Systems, World Scientific (1996).
