Skip to main content

Computing the Edit-Distance between a Regular Language and a Context-Free Language

  • Conference paper
Developments in Language Theory (DLT 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7410))

Included in the following conference series:

Abstract

The edit-distance between two strings is the smallest number of operations required to transform one string into the other. The edit-distance problem for two languages is to find a pair of strings, each of which is from different language, with the minimum edit-distance. We consider the edit-distance problem for a regular language and a context-free language and present an efficient algorithm that finds an optimal alignment of two strings, each of which is from different language. Moreover, we design a faster algorithm for the edit-distance problem that only finds the minimum number of operations of the optimal alignment.

Han and Ko were supported by the Basic Science Research Program through NRF funded by MEST (2010-0009168). Salomaa was supported by the Natural Sciences and Engineering Research Council of Canada Grant OGP0147224.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Allauzen, C., Mohri, M.: Linear-space computation of the edit-distance between a string and a finite automaton. In: London Algorithmics 2008: Theory and Practice. College Publications (2009)

    Google Scholar 

  2. Alpoge, L., Ang, T., Schaeffer, L., Shallit, J.: Decidability and Shortest Strings in Formal Languages. In: Holzer, M. (ed.) DCFS 2011. LNCS, vol. 6808, pp. 55–67. Springer, Heidelberg (2011)

    Google Scholar 

  3. Bunke, H.: Edit distance of regular languages. In: Proceedings of 5th Annual Symposium on Document Analysis and Information Retrieval, pp. 113–124 (1996)

    Google Scholar 

  4. Hopcroft, J., Ullman, J.: Introduction to Automata Theory, Languages, and Computation, 2nd edn. Addison-Wesley, Reading (1979)

    MATH  Google Scholar 

  5. Kari, L., Konstantinidis, S.: Descriptional complexity of error/edit systems. Journal of Automata, Languages and Combinatorics 9, 293–309 (2004)

    MathSciNet  MATH  Google Scholar 

  6. Konstantinidis, S.: Computing the edit distance of a regular language. Information and Computation 205, 1307–1316 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  7. Levenshtein, V.I.: Binary codes capable of correcting deletions, insertions, and reversals. Soviet Physics Doklady 10(8), 707–710 (1966)

    MathSciNet  Google Scholar 

  8. Mohri, M.: Semiring frameworks and algorithms for shortest-distance problems. Journal of Automata, Languages and Combinatorics 7, 321–350 (2002)

    MathSciNet  MATH  Google Scholar 

  9. Mohri, M.: Edit-distance of weighted automata: General definitions and algorithms. International Journal of Foundations of Computer Science 14(6), 957–982 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  10. Pevzner, P.A.: Computational Molecular Biology: An Algorithmic Approach (Computational Molecular Biology). The MIT Press (2000)

    Google Scholar 

  11. Pighizzini, G.: How hard is computing the edit distance? Information and Computation 165(1), 1–13 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  12. Thompson, K.: Programming techniques: Regular expression search algorithm. Communications of the ACM 11, 419–422 (1968)

    Article  MATH  Google Scholar 

  13. Wagner, R.A.: Order-n correction for regular languages. Communications of the ACM 17, 265–268 (1974)

    Article  MATH  Google Scholar 

  14. Wagner, R.A., Fischer, M.J.: The string-to-string correction problem. Journal of the ACM 21, 168–173 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  15. Wood, D.: Theory of Computation. Harper & Row (1987)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Han, YS., Ko, SK., Salomaa, K. (2012). Computing the Edit-Distance between a Regular Language and a Context-Free Language. In: Yen, HC., Ibarra, O.H. (eds) Developments in Language Theory. DLT 2012. Lecture Notes in Computer Science, vol 7410. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31653-1_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-31653-1_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31652-4

  • Online ISBN: 978-3-642-31653-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics