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Relative Prefix Distance Between Languages

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Developments in Language Theory (DLT 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10396))

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Abstract

The prefix distance between two words x and y is defined as the number of symbols in x and y that do not belong to their longest common prefix. The relative prefix distance from a language \(L_1\) to a language \(L_2\), if finite, is the smallest integer k such that for every word in \(L_1\), there is a word in \(L_2\) with prefix distance at most k. We study the prefix distance between regular, visibly pushdown, deterministic context-free, and context-free languages. We show how to compute the distance between regular languages and determine whether the distance is bounded. For deterministic context-free languages and visibly pushdown languages, we show that the relative prefix distance to and from regular languages is decidable.

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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 Timothy Ng .

Editor information

Editors and Affiliations

  1. Université de Liège, Liège, Belgium

    Émilie Charlier

  2. Université de Liège, Liège, Belgium

    Julien Leroy

  3. Université de Liège, Liège, Belgium

    Michel Rigo

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Ng, T., Rappaport, D., Salomaa, K. (2017). Relative Prefix Distance Between Languages. In: Charlier, É., Leroy, J., Rigo, M. (eds) Developments in Language Theory. DLT 2017. Lecture Notes in Computer Science(), vol 10396. Springer, Cham. https://doi.org/10.1007/978-3-319-62809-7_21

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  • DOI: https://doi.org/10.1007/978-3-319-62809-7_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-62808-0

  • Online ISBN: 978-3-319-62809-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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