Nondeterministic Complexity of Operations on Free and Convex Languages

  • Michal HospodárEmail author
  • Galina Jirásková
  • Peter Mlynárčik
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10329)


We study the nondeterministic state complexity of basic regular operations on the classes of prefix-, suffix-, factor-, and subword-free and -convex regular languages. For the operations of intersection, union, concatenation, square, star, reversal, and complementation, we get the tight upper bounds for all considered classes except for complementation on factor- and subword-convex languages. Most of our witnesses are described over optimal alphabets. The most interesting result is the describing of a proper suffix-convex language over a five-letter alphabet meeting the upper bound \(2^n\) for complementation.


Regular Language Deterministic Finite Automaton Binary Alphabet Ideal Language Nondeterministic Finite Automaton 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We would like to thank Jozef Jirásek, Jr., for his help with finding the suffix-convex witness for complementation and for fruitful discussions on the topic.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Michal Hospodár
    • 1
    Email author
  • Galina Jirásková
    • 1
  • Peter Mlynárčik
    • 1
  1. 1.Mathematical InstituteSlovak Academy of SciencesKošiceSlovakia

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