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State Complexity of Prefix Distance

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Implementation and Application of Automata (CIAA 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9223))

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Abstract

The prefix distance between strings x and y is the number of symbol occurrences in the strings that do not belong to the longest common prefix of x and y. The suffix and the substring distance are defined analogously in terms of the longest common suffix and longest common substring, respectively, of two strings. We show that the set of strings within prefix distance k from an n state DFA (deterministic finite automaton) language can be recognized by a DFA with \((k+1) \cdot n - \frac{k(k+1)}{2}\) states and this number of states is needed in the worst case. Also we give tight bounds for the nondeterministic state complexity of the set of strings within prefix, suffix or substring distance k from a regular language.

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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

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  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. Umeå University, Umeå, Sweden

    Frank Drewes

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Ng, T., Rappaport, D., Salomaa, K. (2015). State Complexity of Prefix Distance. In: Drewes, F. (eds) Implementation and Application of Automata. CIAA 2015. Lecture Notes in Computer Science(), vol 9223. Springer, Cham. https://doi.org/10.1007/978-3-319-22360-5_20

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  • DOI: https://doi.org/10.1007/978-3-319-22360-5_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22359-9

  • Online ISBN: 978-3-319-22360-5

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