Approximate string matching by finite automata

  • Bořivoj Melichar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 970)

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. [AU71,2]
    Aho, A., Ullman, J.: The theory of parsing, translation and compiling. Vol. I: Parsing, Prentice Hall, Englewood Cliffs, New York 1972.Google Scholar
  2. [BG92]
    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. [MW92]
    Manber, U., Wu, S.: Approximate pattern matching. BYTE, November 1992, pp. 281–292.Google Scholar
  4. [Uk85]
    Ukkonen, E.: Finding approximate patterns in strings. Journal of algorithms 6, 1985, pp. 132–137.Google Scholar
  5. [WF74]
    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. [WM92]
    Wu, S., Manber, U.: Fast text searching allowing errors. Communications of the ACM, October 1992, Vol. 35, No. 10, pp. 83–91.Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Bořivoj Melichar
    • 1
  1. 1.Department of Computer Science and Engineering, Faculty of Electrical EngineeringCzech Technical UniversityPrague 2Czech Republic

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