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The Ranges of Accepting State Complexities of Languages Resulting From Some Operations

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Implementation and Application of Automata (CIAA 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10977))

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Abstract

We examine the accepting state complexity, i.e., the minimal number of accepting states of deterministic finite automata (DFAs) for languages resulting from unary and binary operations on languages with accepting state complexity given as a parameter. This is continuation of the work of [J. Dassow: On the number of accepting states of finite automata, J. Autom., Lang. Comb., 21, 2016]. We solve most of the open problems mentioned thereof. In particular, we consider the operations of intersection, symmetric difference, right and left quotients, reversal, and permutation (on finite languages), where we obtain precise ranges of the accepting state complexities.

M. Hospodár—Research supported by VEGA grant 2/0084/15 and grant APVV-15-0091. This work was conducted during a research visit at the Institut für Informatik, Universität Giessen, Germany, funded by the DAAD short-term grant ID 57314022.

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Authors and Affiliations

  1. Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, 040 01, Košice, Slovakia

    Michal Hospodár

  2. Institut für Informatik, Universität Giessen, Arndtstr. 2, 35392, Giessen, Germany

    Markus Holzer

Authors
  1. Michal Hospodár
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  2. Markus Holzer
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Correspondence to Markus Holzer .

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Editors and Affiliations

  1. University of Prince Edward Island, Charlottetown, Prince Edward Island, Canada

    Cezar Câmpeanu

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Hospodár, M., Holzer, M. (2018). The Ranges of Accepting State Complexities of Languages Resulting From Some Operations. In: Câmpeanu, C. (eds) Implementation and Application of Automata. CIAA 2018. Lecture Notes in Computer Science(), vol 10977. Springer, Cham. https://doi.org/10.1007/978-3-319-94812-6_17

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  • DOI: https://doi.org/10.1007/978-3-319-94812-6_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-94811-9

  • Online ISBN: 978-3-319-94812-6

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