Abstract
Tiling systems that recognize two-dimensional languages are intrinsically non-deterministic models. We introduce the notion of deterministic tiling system that generalizes deterministic automata for strings. The corresponding family of languages matches all the requirements of a robust deterministic class. Furthermore we show that, differently from the one-dimensional case, there exist many classes between deterministic and non-deterministic families that we separate by means of examples and decidability properties.
This work was partially supported by PRIN project Linguaggi Formali e Automi: aspetti matematici e applicativi.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Anselmo, M., Giammarresi, D., Madonia, M., Restivo, A.: Unambiguous Recognizable Two-dimensional Languages. RAIRO: Theoretical Informatics and Applications EDP Sciences 2006 40(2), 227–294 (2006)
Bertoni, A., Goldwurm, M., Lonati, V.: On the complexity of unary tiling-recognizable picture languages. In: Thomas, W., Weil, P. (eds.) STACS 2007. LNCS, vol. 4393, Springer-Verlag, Heidelberg (To appear, 2007)
Blum, M., Hewitt, C.: Automata on a two-dimensional tape. IEEE Symposium on Switching and Automata Theory, pp. 155–160 (1967)
Borchert, B., Reinhardt, K.: Deterministically and Sudoku-Deterministically Recognizable Picture Languages, http://www-fs.informatik.uni-tuebingen.de/~borchert/papers/Borchert-Reinhardt_2006_Sudoku.pdf
Eilenberg, S.: Automata, Languages and Machines, vol. A. Academic Press, London (1974)
Giammarresi, D., Restivo, A.: Recognizable picture languages. Int. Journal Pattern Recognition and Artificial Intelligence 6(2,3), 241–256 (1992)
Giammarresi, D., Restivo, A.: Two-dimensional languages. In: Rozenberg, G., et al. (ed.) Handbook of Formal Languages, vol. III, pp. 215–268. Springer Verlag, Heidelberg (1997)
Inoue, K., Nakamura, A.: Some properties of two-dimensional on-line tessellation acceptors. Information Sciences 13, 95–121 (1977)
Inoue, K., Nakamura, A.: Nonclosure properties of two-dimensional on-line tessellation acceptors and one-way parallel/sequential array acceptors. Transaction of IECE of Japan 6, 475–476 (1977)
Inoue, K., Takanami, I.: A characterization of recognizable picture languages. In: Nakamura, A., Saoudi, A., Inoue, K., Wang, P.S.P., Nivat, M. (eds.) ICPIA 1992. LNCS, vol. 654, Springer-Verlag, Berlin Heidelberg (1993)
Lindgren, K., Moore, C., Nordahl, M.: Complexity of two-dimensional patterns. Journal of Statistical Physics 91(5-6), 909–951 (1998)
Matz, O.: On piecewise testable, starfree, and recognizable picture languages. In: Nivat, M. (ed.) ETAPS 1998 and FOSSACS 1998. LNCS, vol. 1378, Springer, Heidelberg (1998)
Potthoff, A., Seibert, S., Thomas, W.: Nondeterminism versus determinism of finite automata over directed acyclic graphs. Bull. Belgian Math. Soc. 1, 285–298 (1994)
Reinhardt, K.: On some recognizable picture-languages. In: Brim, L., Gruska, J., Zlatuška, J. (eds.) MFCS 1998. LNCS, vol. 1450, pp. 760–770. Springer, Heidelberg (1998)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Anselmo, M., Giammarresi, D., Madonia, M. (2007). From Determinism to Non-determinism in Recognizable Two-Dimensional Languages. In: Harju, T., Karhumäki, J., Lepistö, A. (eds) Developments in Language Theory. DLT 2007. Lecture Notes in Computer Science, vol 4588. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73208-2_7
Download citation
DOI: https://doi.org/10.1007/978-3-540-73208-2_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73207-5
Online ISBN: 978-3-540-73208-2
eBook Packages: Computer ScienceComputer Science (R0)