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Quasi-Distances and Weighted Finite Automata

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Descriptional Complexity of Formal Systems (DCFS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9118))

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Abstract

We show that the neighbourhood of a regular language \(L\) with respect to an additive quasi-distance can be recognized by an additive weighted finite automaton (WFA). The size of the WFA is the same as the size of an NFA (nondeterministic finite automaton) for \(L\) and the construction gives an upper bound for the state complexity of a neighbourhood of a regular language with respect to a quasi-distance. We give a tight lower bound construction for the determinization of an additive WFA using an alphabet of size five. The previously known lower bound construction needed an alphabet that is linear in the number of states of the WFA.

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Notes

  1. 1.

    Theorem 8 of [2] assumes that \(N\) is deterministic. However, the construction used in the proof works also for an NFA.

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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. School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada

    Jeffrey Shallit

  2. Department of Mathematics, University of Turku, Turku, Finland

    Alexander Okhotin

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Ng, T., Rappaport, D., Salomaa, K. (2015). Quasi-Distances and Weighted Finite Automata. In: Shallit, J., Okhotin, A. (eds) Descriptional Complexity of Formal Systems. DCFS 2015. Lecture Notes in Computer Science(), vol 9118. Springer, Cham. https://doi.org/10.1007/978-3-319-19225-3_18

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  • DOI: https://doi.org/10.1007/978-3-319-19225-3_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19224-6

  • Online ISBN: 978-3-319-19225-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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