Abstract
In this article, we study classes of multidimensional subshifts defined by multihead finite automata, in particular the hierarchy of classes of subshifts defined as the number of heads grows. The hierarchy collapses on the third level, where all co-recursively enumerable subshifts are obtained in every dimension. We also compare these classes to SFTs and sofic shifts. We are unable to separate the second and third level of the hierarchy in one and two dimensions, and suggest a related open problem for two-counter machines.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Strictly speaking, they were augmented by markers, but the difference is small.
References
Blum, M., Hewitt, C.: Automata on a 2-dimensional tape. In: IEEE Conference Record of the Eighth Annual Symposium on Switching and Automata Theory, SWAT 1967, pp. 155–160, October 1967
Bojańczyk, M.: Tree-walking automata. In: Martín-Vide, C., Otto, F., Fernau, H. (eds.) LATA 2008. LNCS, vol. 5196, pp. 1–2. Springer, Heidelberg (2008)
Bojańczyk, M., Colcombet, T.: Tree-walking automata do not recognize all regular languages. SIAM J. Comput. 38(2), 658–701 (2008)
Bojańczyk, M., Samuelides, M., Schwentick, T., Segoufin, L.: Expressive power of pebble automata. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4051, pp. 157–168. Springer, Heidelberg (2006)
Conway, J.H.: Fractran: a simple universal programming language for arithmetic. In: Cover, T.M., Gopinath, B. (eds.) Open Problems in Communication and Computation, pp. 4–26. Springer-Verlag New York Inc., New York (1987)
Giammarresi, D., Venezia, F., Restivo, A.: Two-dimensional languages (1997)
Holzer, M., Kutrib, M., Malcher, A.: Multi-head finite automata: characterizations, concepts and open problems. ArXiv e-prints, June 2009
Hsia, P., Yeh, R.T.: Marker automata. Inform. Sci. 8(1), 71–88 (1975)
Ibarra, O.H., Trân, N.Q.: A note on simple programs with two variables. Theor. Comput. Sci. 112(2), 391–397 (1993)
Inoue, K., Takanami, I.: A survey of two-dimensional automata theory. Inform. Sci. 55(1–3), 99–121 (1991)
Kari, J., Salo, V.: A survey on picture-walking automata. In: Kuich, W., Rahonis, G. (eds.) Algebraic Foundations in Computer Science. LNCS, vol. 7020, pp. 183–213. Springer, Heidelberg (2011)
Kass, S., Madden, K.: A sufficient condition for non-soficness of higher-dimensional subshifts. Proc. Amer. Math. Soc. 141(11), 3803–3816 (2013)
Pavlov, R., Schraudner, M.: Classification of sofic projective subdynamics of multidimensional shifts of finite type (submitted)
Salo, V., Törmä, I.: Commutators of bipermutive and affine cellular automata. In: Kari, J., Kutrib, M., Malcher, A. (eds.) AUTOMATA 2013. LNCS, vol. 8155, pp. 155–170. Springer, Heidelberg (2013)
Schroeppel, R.: A two counter machine cannot calculate \(2^N\) (1972)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Salo, V., Törmä, I. (2015). Plane-Walking Automata. In: Isokawa, T., Imai, K., Matsui, N., Peper, F., Umeo, H. (eds) Cellular Automata and Discrete Complex Systems. AUTOMATA 2014. Lecture Notes in Computer Science(), vol 8996. Springer, Cham. https://doi.org/10.1007/978-3-319-18812-6_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-18812-6_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-18811-9
Online ISBN: 978-3-319-18812-6
eBook Packages: Computer ScienceComputer Science (R0)