Abstract
The class of regular word languages plays a central role in formal language theory. Considerable effort has been made to transfer definitions and applications from word languages to their two-dimensional analog, the picture languages, where one considers (two-dimensional) matrices rather than (one-dimensional) words.
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References
Anselmo, M., Giammarresi, D., Madonia, M.: New operations and regular expressions for two-dimensional languages over one-letter alphabet. Theor. Comput. Sci. 340(1), 408–431 (2005)
Anselmo, M., Giammarresi, D., Madonia, M.: From determinism to non-determinism in recognizable two-dimensional languages. In: Developments in Language Theory. Springer, Heidelberg (to appear, 2007)
Anselmo, M., Giammarresi, D., Madonia, M., Restivo, A.: Unambigiuos recognizable two-dimensional languages. Inf. Theor. Appl. 40, 277–293 (2006)
Anselmo, M., Madonia, M.: Deterministic two-dimensional languages over one-letter alphabet. In: CD proceedings of CAI (2007)
Borchert, B., Reinhardt, K.: Deterministically and sudoku-deterministically recognizable picture languages (2006), http://tobias-lib.ub.uni-tuebingen.de/volltexte/2006/2503/
Bozapalidis, S., Grammatikopoulou, A.: Recognizable picture series. Journal of Automata, Languages and Combinatorics 10(2/3), 159–183 (2005)
Giammarresi, D.: Two-dimensional languages and recognizable functions. In: Rozenberg, G., Salomaa, A. (eds.) Developments in Language Theory, Proceedings of the conference, Turku (Finnland), 1993, pp. 290–301. world scientific, Singapore (1994)
Giammarresi, D.: Tiling recognizable two-dimensional languages (included in these proceedings). Springer, Heidelberg (2007)
Giammarresi, D., Restivo, A.: Recognizable picture languages. In: Proceedings First International Colloqium on Parallel Image Processing 1991. International Journal Pattern Recognition and Artificial Intelligence, vol. 6, pp. 241–256 (1992)
Giammarresi, D., Restivo, A.: Two-dimensional languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Language Theory, vol. III, pp. 215–268. Springer, New York (1996)
Giammarresi, D., Restivo, A., Seibert, S., Thomas, W.: Monadic second-order logic and recognizability by tiling systems. Information and Computation 125, 32–45 (1996)
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., Nakamura, A.: Some properties of two-dimensional on-line tessellation acceptors. Information Sciences 13, 95–121 (1977)
Inoue, K., Takanami, I.: A survey of two-dimensional automata theory. In: Dassow, J., Kelemen, J. (eds.) Proceedings 5th International Meeting of Young Computer Scientists. 5th International Meeting of Young Computer Scientists. LNCS, vol. 381, pp. 72–91. Springer, Heidelberg (1990)
Inoue, K., Takanami, I.: A characterization of recognizable picture languages. In: Dassow, J., Kelemen, J. (eds.) Machines, Languages, and Complexity. LNCS, vol. 381, pp. 133–143. Springer, Heidelberg (1992)
Latteux, M., Simplot, D.: Context-sensitive string languages and recognizable picture languages. Information and Computation 138, 160–169 (1997)
Latteux, M., Simplot, D.: Recognizable picture languages and domino tiling. Theoretical Computer Science 178(1-2), 275–283 (1997)
Matz, O.: Klassifizierung von Bildsprachen mit rationalen Ausdrücken, Grammatiken und Logik-Formeln. Diploma thesis, Christian-Albrechts-Universität Kiel (in German) (1995)
Matz, O.: Regular expressions and context-free grammars for picture languages. In: Reischuk, R., Morvan, M. (eds.) STACS 1997. LNCS, vol. 1200, pp. 283–294. Springer, Heidelberg (1997)
Matz, O.: On piecewise testable, starfree, and recognizable picture languages. In: Nivat, M. (ed.) ETAPS 1998 and FOSSACS 1998. LNCS, vol. 1378, pp. 203–210. Springer, Heidelberg (1998)
Matz, O.: One quantifier will do in existential monadic second-order logic over pictures. In: Brim, L., Gruska, J., Zlatuška, J. (eds.) MFCS 1998. LNCS, vol. 1450, pp. 751–759. Springer, Heidelberg (1998)
Matz, O.: Dot-depth, monadic quantifier alternation, and first-order closure over grids and pictures. Theor. Comput. Sci. 270(1-2), 1–70 (2002)
Matz, O.: A Kleene theorem for regular picture languages. Technical Report 0703, Christian-Albrechts-Universität Kiel (2007)
Matz, O., Thomas, W.: The monadic quantifier alternation hierarchy over graphs is infinite. In: Twelfth Annual IEEE Symposium on Logic in Computer Science, Warsaw, Poland, pp. 236–244. IEEE Computer Society Press, Los Alamitos (1997)
Prophetis de, L., Varricchio, S.: Recognizability of rectangular pictures by wang systems. Journal of Automata, Languages and Combinatorics 2, 269–288 (1997)
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)
Reinhardt, K.: The #a = #b pictures are recognizable. In: Symposium on Theoretical Aspects of Computer Science, pp. 527–538 (2001)
Schweikardt, N.: The monadic quantifier alternation hierarchy over grids and pictures. In: Nielsen, M. (ed.) CSL 1997. LNCS, vol. 1414, pp. 441–460. Springer, Heidelberg (1998)
Simplot, D.: A characterization of recognizable picture languages by tilings by finite sets. Theoretical Computer Science 218(2), 297–323 (1999)
Siromoney, R.: Advances in array languages. In: Ehrig, H., Nagl, M., Rosenfeld, A., Rozenberg, G. (eds.) Graph-Grammars and Their Application to Computer Science. LNCS, vol. 291, pp. 549–563. Springer, Heidelberg (1987)
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Matz, O. (2007). Recognizable vs. Regular Picture Languages. In: Bozapalidis, S., Rahonis, G. (eds) Algebraic Informatics. CAI 2007. Lecture Notes in Computer Science, vol 4728. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75414-5_7
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DOI: https://doi.org/10.1007/978-3-540-75414-5_7
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