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State Complexity of Neighbourhoods and Approximate Pattern Matching

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Developments in Language Theory (DLT 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9168))

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Abstract

The neighbourhood of a language L with respect to an additive distance consists of all strings that have distance at most the given radius from some string of L. We show that the worst case (deterministic) state complexity of a radius r neighbourhood of a language recognized by an n state nondeterministic finite automaton A is \((r+2)^n\). The lower bound construction uses an alphabet of size linear in n. We show that the worst case state complexity of the set of strings that contain a substring within distance r from a string recognized by A is \((r+2)^{n-2} + 1\).

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Authors and Affiliations

  1. School of Computing, Queen’s University, Kingston, ON, K7L 3N6, Canada

    Timothy Ng, David Rappaport & Kai Salomaa

Authors
  1. Timothy Ng
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  2. David Rappaport
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  3. Kai Salomaa
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Corresponding author

Correspondence to Kai Salomaa .

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Editors and Affiliations

  1. University of Liverpool, Liverpool, United Kingdom

    Igor Potapov

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© 2015 Springer International Publishing Switzerland

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Ng, T., Rappaport, D., Salomaa, K. (2015). State Complexity of Neighbourhoods and Approximate Pattern Matching. In: Potapov, I. (eds) Developments in Language Theory. DLT 2015. Lecture Notes in Computer Science(), vol 9168. Springer, Cham. https://doi.org/10.1007/978-3-319-21500-6_31

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  • DOI: https://doi.org/10.1007/978-3-319-21500-6_31

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21499-3

  • Online ISBN: 978-3-319-21500-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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