Abstract
We study the two-dimensional pattern matching implemented using the two-dimensional on-line tessellation automaton, which is a restricted type of the cellular automaton able to simulate the Baker-Bird algorithm, proposed as the first algorithm for the two-dimensional pattern matching. We further explore capabilities of this automaton to carry out the matching task against an arbitrary set of equally sized patterns. To measure amount of resources needed to accomplish it, we introduce the pattern complexity of a picture language. We show that this complexity spreads in a wide range. It is demonstrated by giving examples, deriving general techniques and proving some lower bounds.
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References
Aho, A.V., Corasick, M.J.: Efficient string matching: An aid to bibliographic search. Commun. ACM 18(6), 333–340 (1975). http://doi.acm.org/10.1145/360825.360855
Amir, A., Benson, G., Farach, M.: Alphabet independent two dimensional matching. In: Proceedings of the Twenty-Fourth Annual ACM Symposium on Theory of Computing, STOC 1992, pp. 59–68. ACM, New York (1992). http://doi.acm.org/10.1145/129712.129719
Baeza-Yates, R., Régnier, M.: Fast two-dimensional pattern matching. Inf. Process. Lett. 45(1), 51–57 (1993). http://www.sciencedirect.com/science/article/pii/002001909390250D
Baker, T.P.: A technique for extending rapid exact-match string matching to arrays of more than one dimension. SIAM J. Comput. 7(4), 533–541 (1978). http://dx.doi.org/10.1137/0207043
Bird, R.S.: Two dimensional pattern matching. Inf. Process. Lett. 6(5), 168–170 (1977). http://dx.doi.org/10.1016/0020-0190(77)90017-5
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)
Inoue, K., Nakamura, A.: Some properties of two-dimensional on-line tessellation acceptors. Inf. Sci. 13(2), 95–121 (1977)
Kärkkäinen, J., Ukkonen, E.: Two and higher dimensional pattern matching in optimal expected time. In: Sleator, D.D. (ed.) Proceedings of the Fifth Annual ACM-SIAM Symposium on Discrete Algorithms. 23–25 January 1994, Arlington, Virginia, pp. 715–723. ACM/SIAM (1994). http://dl.acm.org/citation.cfm?id=314464.314680
Li, M., Vitnyi, P.M.: An Introduction to Kolmogorov Complexity and its Applications, 3rd edn. Springer Publishing Company, Incorporated, New York (2008)
Polcar, T., Melichar, B.: Two-dimensional pattern matching by two-dimensional online tessellation automata. In: Domaratzki, M., Okhotin, A., Salomaa, K., Yu, S. (eds.) CIAA 2004. LNCS, vol. 3317, pp. 327–328. Springer, Heidelberg (2005). http://dx.doi.org/10.1007/978-3-540-30500-2_38
Toda, M., Inoue, K., Takanami, I.: Two-dimensional pattern matching by two-dimensional on-line tessellation acceptors. Theor. Comput. Sci. 24, 179–194 (1983). http://dx.doi.org/10.1016/0304-3975(83)90048–8
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This work was supported by the Czech Science Foundation under grant no. 15-04960S.
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Průša, D. (2016). Complexity of Sets of Two-Dimensional Patterns. In: Han, YS., Salomaa, K. (eds) Implementation and Application of Automata. CIAA 2016. Lecture Notes in Computer Science(), vol 9705. Springer, Cham. https://doi.org/10.1007/978-3-319-40946-7_20
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