Complexity of Bifix-Free Regular Languages

  • Robert Ferens
  • Marek SzykułaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10329)


We study descriptive complexity properties of the class of regular bifix-free languages, which is the intersection of prefix-free and suffix-free regular languages. We show that there exist universal bifix-free languages that meet all the bounds for the state complexity of basic operations (Boolean operations, product, star, and reversal). This is in contrast with suffix-free languages, where it is known that there does not exist such languages. Then we present a stream of bifix-free languages that is most complex in terms of all basic operations, syntactic complexity, and the number of atoms and their complexities, which requires a superexponential alphabet. We also complete the previous results by characterizing state complexity of product, star, and reversal, and establishing tight upper bounds for atom complexities of bifix-free languages. Moreover, we consider the problem of the minimal size of an alphabet required to meet the bounds, and the problem of attainable values of state complexities (magic numbers).


Bifix-free Most complex Prefix-free State complexity Suffix-free Transition semigroup 


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institute of Computer ScienceUniversity of WrocławWrocławPoland

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