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Operations on Boolean and Alternating Finite Automata

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Book cover Computer Science – Theory and Applications (CSR 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10846))

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Abstract

We investigate the descriptional complexity of basic regular operations on languages represented by Boolean and alternating finite automata. In particular, we consider the operations of difference, symmetric difference, star, reversal, left quotient, and right quotient, and get tight upper bounds \(m+n, m+n, 2^n, 2^n, m,\) and \(2^m\), respectively, for Boolean automata, and \(m+n+1, m+n, 2^n, 2^n, m+1\), and \(2^m+1\), respectively, for alternating finite automata. To describe witnesses for symmetric difference, we use a ternary alphabet. All the remaining witnesses are defined over binary or unary alphabets that are shown to be optimal.

Research supported by grant VEGA 2/0084/15 and grant APVV-15-0091. This work was conducted as a part of PhD study of Michal Hospodár and Ivana Krajňáková at the Faculty of Mathematics, Physics and Informatics of the Comenius University.

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Authors and Affiliations

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

    Michal Hospodár, Galina Jirásková & Ivana Krajňáková

Authors
  1. Michal Hospodár
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  2. Galina Jirásková
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  3. Ivana Krajňáková
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Correspondence to Ivana Krajňáková .

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Editors and Affiliations

  1. Department of Informatics, University of Bergen, Bergen, Norway

    Fedor V. Fomin

  2. Steklov Mathematical Institute, Moscow, Russia

    Vladimir V. Podolskii

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Hospodár, M., Jirásková, G., Krajňáková, I. (2018). Operations on Boolean and Alternating Finite Automata. In: Fomin, F., Podolskii, V. (eds) Computer Science – Theory and Applications. CSR 2018. Lecture Notes in Computer Science(), vol 10846. Springer, Cham. https://doi.org/10.1007/978-3-319-90530-3_16

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  • DOI: https://doi.org/10.1007/978-3-319-90530-3_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-90529-7

  • Online ISBN: 978-3-319-90530-3

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