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Approximate string matching by finite automata

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Computer Analysis of Images and Patterns (CAIP 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 970))

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Abstract

Approximate string matching is a sequential problem and therefore it is possible to solve it using finite automata. A nondeterministic finite automaton is constructed for string matching with k mismatches. It is shown, how “dynamic programming” and “shift- and” based algorithms simulate this nondeterministic finite automaton. The corresponding deterministic finite automaton have \(\mathcal{O}(m^{k + 1} )\) states, where m is the length of the pattern and k is the number of mismatches. The time complexity of algorithms based on such deterministic finite automaton is \(\mathcal{O}(n)\), where n is the length of text.

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References

  1. Aho, A., Ullman, J.: The theory of parsing, translation and compiling. Vol. I: Parsing, Prentice Hall, Englewood Cliffs, New York 1972.

    Google Scholar 

  2. Baeza-Yates, R., Gonnet, G. H.: A new approach to text searching. Communications of the ACM, October 1992, Vol. 35, No. 10, pp. 74–82.

    Google Scholar 

  3. Manber, U., Wu, S.: Approximate pattern matching. BYTE, November 1992, pp. 281–292.

    Google Scholar 

  4. Ukkonen, E.: Finding approximate patterns in strings. Journal of algorithms 6, 1985, pp. 132–137.

    Google Scholar 

  5. Wagner, R., A., Fischer, M., J.: The string-to-string correction problem. Journal of the ACM, January 1974, Vol. 21, No. 1, pp. 168–173.

    Google Scholar 

  6. Wu, S., Manber, U.: Fast text searching allowing errors. Communications of the ACM, October 1992, Vol. 35, No. 10, pp. 83–91.

    Google Scholar 

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Václav Hlaváč Radim Šára

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© 1995 Springer-Verlag Berlin Heidelberg

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Melichar, B. (1995). Approximate string matching by finite automata. In: Hlaváč, V., Šára, R. (eds) Computer Analysis of Images and Patterns. CAIP 1995. Lecture Notes in Computer Science, vol 970. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60268-2_315

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  • DOI: https://doi.org/10.1007/3-540-60268-2_315

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60268-2

  • Online ISBN: 978-3-540-44781-8

  • eBook Packages: Springer Book Archive

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