Square on Deterministic, Alternating, and Boolean Finite Automata

  • Ivana KrajňákováEmail author
  • Galina Jirásková
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10316)


We investigate the state complexity of the square operation on languages represented by deterministic, alternating, and Boolean automata. For each k such that \(1 \le k \le n-2\), we describe a binary language accepted by an n-state DFA with k final states meeting the upper bound \(n2^n - k2^{n-1}\) on the state complexity of its square. We show that in the case of \(k=n-1\), the corresponding upper bound cannot be met. Using the DFA witness for square with \(2^n\) states where half of them are final, we get the tight upper bounds on the complexity of the square operation on alternating and Boolean automata.


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Authors and Affiliations

  1. 1.Mathematical InstituteSlovak Academy of SciencesKošiceSlovakia

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