Abstract
This paper presents a general concept of two-dimensional pattern matching using conventional (one-dimensional) finite automata. Then two particular models and methods, implementations of the general principle, are presented. The first of these two models presents an automata based version of the Bird and Baker approach with lower space complexity than the original algorithm. The second introduces a new model for two-dimensional approximate pattern matching using the two-dimensional Hamming distance.
This research is partially supported by the MŠMT under research program MSM 6840770014.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Amir, A.: Theoretical issues of searching aerial photographs: a bird’s eye view. In: Balík, M., Holub, J., Šimánek, M. (eds.) Proceedings of the Prague Stringology Conference 2004, Czech Technical University in Prague, Czech Republic, pp. 1–23 (2004)
Crochemore, M., Hancart, C.: Automata for matching patterns. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, pp. 399–462. Springer, Heidelberg (1997)
Melichar, B.: Approximate string matching by finite automata. In: Hlaváč, V., Šára, R. (eds.) CAIP 1995. LNCS, vol. 970, pp. 342–349. Springer, Heidelberg (1995)
Melichar, B., Holub, J.: 6D classification of pattern matching problems. In: Holub, J. (ed.) Proceedings of the Prague Stringology Club Workshop 1997, Czech Technical University in Prague, Czech Republic, pp. 24–32 (1997)
Giammarresi, D., Restivo, A.: Two-dimensional languages. In: Handbook of Formal Languages, vol. III (Beyond Words), pp. 216–267. Springer, Heidelberg (1997)
Aho, A.V., Corasick, M.J.: Efficient string matching: an aid to bibliographic search. Commun. ACM 18, 333–340 (1975)
Ždárek, J., Melichar, B.: Finite automata and two-dimensional pattern matching. In: Heričko, M., Rozman, I., Jurič, M.B., Rajkovič, V., Urbančič, T., Bernik, M., Bučar, M., Brodnik, A. (eds.) Proceedings of the 7th International Multiconference Information Society IS 2004, Ljubljana, Slovenia, Institut “Jožef Stefan”, vol. D, pp. 185–188 (2004)
Cambouropoulos, E., Crochemore, M., Iliopoulos, C.S., Mouchard, L., Pinzon, Y.J.: Algorithms for computing approximate repetitions in musical sequences. In: Raman, R., Simpson, J. (eds.) Proceedings of the 10th Australasian Workshop On Combinatorial Algorithms, Perth, WA, Australia, pp. 129–144 (1999)
Sellers, P.H.: The theory and computation of evolutionary distances: Pattern recognition. J. Algorithms 1, 359–373 (1980)
Wu, S., Manber, U.: Fast text searching: allowing errors. Commun. ACM 35, 83–91 (1992)
Holub, J.: Simulation of nondeterministic finite automata in pattern matching. Dissertation thesis, Czech Technical University in Prague, Czech Republic (2000)
Knuth, D.E., Morris Jr., J.H., Pratt, V.R.: Fast pattern matching in strings. SIAM J. Comput. 6, 323–350 (1977)
Hamming, R.W.: Error detecting and error correcting codes. The Bell System Technical Journal 29, 147–160 (1950)
Hopcroft, J.E., Ullman, J.D.: Introduction to automata theory, languages and computations. Addison-Wesley, Reading (1979)
Ukkonen, E.: Finding approximate patterns in strings. J. Algorithms 6, 132–137 (1985)
Baeza-Yates, R.A., Navarro, G.: New models and algorithms for multidimensional approximate pattern matching. J. Discret. Algorithms 1, 21–49 (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Žd’árek, J., Melichar, B. (2006). On Two-Dimensional Pattern Matching by Finite Automata. In: Farré, J., Litovsky, I., Schmitz, S. (eds) Implementation and Application of Automata. CIAA 2005. Lecture Notes in Computer Science, vol 3845. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11605157_28
Download citation
DOI: https://doi.org/10.1007/11605157_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-31023-5
Online ISBN: 978-3-540-33097-4
eBook Packages: Computer ScienceComputer Science (R0)