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The Boundary of Prefix-Free Languages

  • Jozef Jirásek
  • Galina JiráskováEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9168)

Abstract

We investigate the boundary operation on the class of prefix-free regular languages. We show that if a prefix-free language is recognized by a deterministic finite automaton of n states, then its boundary is recognized by a deterministic automaton of at most \((n-1)\cdot 2^{n-4}+n+1\) states. We prove that this bound is tight, and to describe worst-case examples, we use a three-letter alphabet. Next we show that the tight bound for boundary on binary prefix-free languages is \(2n-2\), and that in the unary case, the tight bound is \(n-2\).

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institute of Computer Science, Faculty of ScienceP.J. Šafárik UniversityKošiceSlovakia
  2. 2.Mathematical InstituteSlovak Academy of SciencesKošiceSlovakia

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