Operations on Boolean and Alternating Finite Automata

  • Michal Hospodár
  • Galina Jirásková
  • Ivana Krajňáková
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10846)


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.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Michal Hospodár
    • 1
  • Galina Jirásková
    • 1
  • Ivana Krajňáková
    • 1
  1. 1.Mathematical InstituteSlovak Academy of SciencesKošiceSlovakia

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