Abstract
Much work has been done to obtain classes of picture languages that would correspond to the classes of the Chomsky hierarchy for string languages, and finally the class REC of recognizable picture languages has been agreed on as the class that corresponds to the ‘regular string languages.’ This class has several nice characterizations in terms of regular expressions, tiling automata, and on-line tesselation automata, and it has nice closure properties, but it also has two main drawbacks: all its characterizations are highly nondeterministic in nature, and it contains languages that are NP-complete. Consequentially, various deterministic subclasses of REC have been defined. Mainly, however, these definitions are quite complex, and it is not clear which of the resulting classes should be considered as ‘the’ class of deterministic recognizable picture languages. Here we present some recent developments obtained in a research project that aims at finding a deterministic model of a two-dimensional automaton that has the following desirable properties:
-
the automaton should be conceptually simple,
-
the class of languages accepted should be as large as possible,
-
it should have nice closure properties,
-
the membership problem for each of these languages should be solvable in polynomial time,
-
but when restricted to one-row pictures (that is, strings), only the regular languages should be accepted.
In the course of the project, several types of two-dimensional automata have been defined and investigated. Here these types of automata and the classes of picture languages accepted by them are compared to each other and to the classes REC and DREC, and their closure properties and algorithmic properties are considered.
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.: From determinism to non-determinism in recognizable two-dimensional languages. In: Harju, T., Karhumäki, J., Lepistö, A. (eds.) DLT 2007. LNCS, vol. 4588, pp. 36–47. Springer, Heidelberg (2007)
Anselmo, A., Giammarresi, D., Madonia, M.: A computational model for tiling recognizable two-dimensional languages. Theor. Comput. Sci. 410, 3520–3529 (2009)
Blum, M., Hewitt, C.: Automata on a 2-dimensional tape. In: SWAT 1967, pp. 155–160. IEEE Computer Society, Washington, DC (1967)
Borchert, B., Reinhardt, K.: Deterministically and sudoku-deterministically recognizable picture languages. In: Loos, R., Fazekas, S., Martín-Vide, C. (eds.) LATA 2007, Preproc. Report 35/07, pp. 175–186. Research Group on Mathematical Linguistics, Universitat Rovira i Virgili, Tarragona (2007)
Cherubini, A., Pradella, M.: Picture Languages: From Wang Tiles to 2D Grammars. In: Bozapalidis, S., Rahonis, G. (eds.) CAI 2009. LNCS, vol. 5725, pp. 13–46. Springer, Heidelberg (2009)
Giammarresi, D., Restivo, A.: Recognizable picture languages. Intern. J. Pattern Recognition and Artificial Intelligence 6(2-3), 241–256 (1992)
Giammarresi, D., Restivo, A.: Two-dimensional languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. 3, pp. 215–267. Springer, New York (1997)
Hennie, F.: One-tape, off-line Turing machine computations. Informat. Control 8(6), 553–578 (1965)
Hopcroft, J., Ullman, J.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading (1979)
Inoue, K., Nakamura, A.: Some properties of two-dimensional on-line tessellation acceptors. Inform. Sci. 13, 95–121 (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, pp. 133–143. Springer, Heidelberg (1992)
Jančar, P., Mráz, F., Plátek, M.: Characterization of context-free languages by erasing automata. In: Havel, I.M., Koubek, V. (eds.) MFCS 1992. LNCS, vol. 629, pp. 307–314. Springer, Heidelberg (1992)
Jančar, P., Mráz, F., Plátek, M., Vogel, J.: Restarting automata. In: Reichel, H. (ed.) FCT 1995. LNCS, vol. 965, pp. 283–292. Springer, Heidelberg (1995)
Jiřička, P., Král, J.: Deterministic forgetting planar automata are more powerful than non-deterministic finite-state planar automata. In: Rozenberg, G., Thomas, W. (eds.) DLT 1999, pp. 71–80. World Scientific, Singapore (2000)
Kari, J., Moore, C.: New results on alternating and non-deterministic two-dimensional finite-state automata. In: Ferreira, A., Reichel, H. (eds.) STACS 2001. LNCS, vol. 2010, pp. 396–406. Springer, Heidelberg (2001)
Lindgren, K., Moore, C., Nordahl, M.: Complexity of two-dimensional patterns. J. Stat. Phys. 91(5-6), 909–951 (1998)
Messerschmidt, H., Stommel, M.: Church-Rosser picture languages and their applications in picture recognition. J. Autom. Lang. Comb. 16, 165–194 (2011)
Otto, F., Mráz, F.: Extended two-way ordered restarting automata for picture languages. In: Dediu, A.-H., Martín-Vide, C., Sierra-Rodríguez, J.-L., Truthe, B. (eds.) LATA 2014. LNCS, vol. 8370, pp. 541–552. Springer, Heidelberg (2014)
Mráz, F., Otto, F.: Ordered restarting automata for picture languages. In: Geffert, V., Preneel, B., Rovan, B., Štuller, J., Tjoa, A.M. (eds.) SOFSEM 2014. LNCS, vol. 8327, pp. 431–442. Springer, Heidelberg (2014)
Otto, F.: Restarting automata. In: Ésik, Z., Martín-Vide, C., Mitrana, V. (eds.) Recent Advances in Formal Languages and Applications. SCI, vol. 25, pp. 269–303. Springer, Heidelberg (2006)
Průša, D.: Weight-reducing Hennie machines and their descriptional complexity. In: Dediu, A.-H., Martín-Vide, C., Sierra-Rodríguez, J.-L., Truthe, B. (eds.) LATA 2014. LNCS, vol. 8370, pp. 553–564. Springer, Heidelberg (2014)
Průša, D., Mráz, F.: Restarting tiling automata. In: Moreira, N., Reis, R. (eds.) CIAA 2012. LNCS, vol. 7381, pp. 289–300. Springer, Heidelberg (2012)
Průša, D., Mráz, F.: Two-dimensional sgraffito automata. In: Yen, H.-C., Ibarra, O.H. (eds.) DLT 2012. LNCS, vol. 7410, pp. 251–262. Springer, Heidelberg (2012)
Průša, D., Mráz, F.: Restarting tiling automata. Intern. J. Found. Comput. Sci. 24(6), 863–878 (2013)
Průša, D., Mráz, F., Otto, F.: Comparing two-dimensional one-marker automata to sgraffito automata. In: Konstantinidis, S. (ed.) CIAA 2013. LNCS, vol. 7982, pp. 268–279. Springer, Heidelberg (2013)
Průša, D., Mráz, F., Otto, F.: New results on deterministic sgraffito automata. In: Béal, M.-P., Carton, O. (eds.) DLT 2013. LNCS, vol. 7907, pp. 409–419. Springer, Heidelberg (2013)
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)
Rosenfeld, A.: Isotonic grammars, parallel grammars, and picture grammars. In: Meltzer, B., Michie, D. (eds.) Machine Intelligence, vol. 6, pp. 281–294. Edinburgh University Press (1971)
Siromoney, G., Siromoney, R., Krithivasan, K.: Abstract families of matrices and picture languages. Computer Graphics and Image Processing 1(3), 284–307 (1972)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Otto, F. (2014). Restarting Automata for Picture Languages: A Survey on Recent Developments. In: Holzer, M., Kutrib, M. (eds) Implementation and Application of Automata. CIAA 2014. Lecture Notes in Computer Science, vol 8587. Springer, Cham. https://doi.org/10.1007/978-3-319-08846-4_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-08846-4_2
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-08845-7
Online ISBN: 978-3-319-08846-4
eBook Packages: Computer ScienceComputer Science (R0)