The Complexity of Languages Resulting from the Concatenation Operation

  • Galina JiráskováEmail author
  • Alexander Szabari
  • Juraj Šebej
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9777)


We prove that for all mn, and \(\alpha \) with \(1 \le \alpha \le f(m,n)\), where f(mn) is the state complexity of the concatenation operation, there exist a minimal m-state DFA A and a minimal n-state DFA B, both defined over an alphabet \(\varSigma \) with \(|\varSigma |\le 2n+4\), such that the minimal DFA for the language L(A)L(B) has exactly \(\alpha \) states. This improves a similar result in the literature that uses an exponential alphabet.


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Copyright information

© IFIP International Federation for Information Processing 2016

Authors and Affiliations

  • Galina Jirásková
    • 1
    Email author
  • Alexander Szabari
    • 2
  • Juraj Šebej
    • 2
  1. 1.Mathematical InstituteSlovak Academy of SciencesKošiceSlovakia
  2. 2.Faculty of Science, Institute of Computer ScienceP.J. Šafárik UniversityKošiceSlovakia

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