Nondeterministic Complexity of Operations on Closed and Ideal Languages

  • Michal Hospodár
  • Galina Jirásková
  • Peter Mlynárčik
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9705)


We study the nondeterministic state complexity of basic regular operations on the classes of prefix-, suffix-, factor-, and subword-closed regular languages and on the classes of right, left, two-sided, and all-sided ideal regular languages. For the operations of union, intersection, complementation, concatenation, square, star, and reversal, we get the tight upper bounds for all considered classes.


Basic Operation Regular Language Arbitrary Positive Integer Short String Regular Operation 
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  1. 1.
    Birget, J.C.: Partial orders on words, minimal elements of regular languages, and state complexity. Theoret. Comput. Sci. 119, 267–291 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Brzozowski, J., Jirásková, G., Li, B.: Quotient complexity of ideal languages. Theoret. Comput. Sci. 470, 36–52 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Brzozowski, J., Jirásková, G., Zou, C.: Quotient complexity of closed languages. Theor. Comput. Syst. 54, 277–292 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Čevorová, K.: Square on ideal, closed and free languages. In: Shallit, J., Okhotin, A. (eds.) DCFS 2015. LNCS, vol. 9118, pp. 70–80. Springer, Heidelberg (2015)CrossRefGoogle Scholar
  5. 5.
    Čevorová, K., Jirásková, G., Mlynárčik, P., Palmovský, M., Šebej, J.: Operations on automata with all states final. In: Ésik, Z., Fülöp, Z. (eds.) Automata and Formal Languages 2014 (AFL 2014). EPTCS, vol. 151, pp. 201–215 (2014)Google Scholar
  6. 6.
    Han, Y.-S., Salomaa, K.: Nondeterministic state complexity for suffix-free regular languages. In: DCFS 2010, pp. 189–196 (2010)Google Scholar
  7. 7.
    Han, Y.-S., Salomaa, K., Wood, D.: Nondeterministic state complexity of basic operations for prefix-free regular languages. Fundam. Inform. 90(1–2), 93–106 (2009)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Holzer, M., Kutrib, M.: Nondeterministic descriptional complexity of regular languages. Int. J. Found. Comput. Sci. 14, 1087–1102 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Jirásková, G.: State complexity of some operations on binary regular languages. Theoret. Comput. Sci. 330, 287–298 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Jirásková, G.: Note on minimal automata and uniform communication protocols. In: Grammars and Automata for String Processing: From Mathematics and Computer Science to Biology, and Back, pp. 163–170. Taylor and Francis (2003)Google Scholar
  11. 11.
    Jirásková, G., Masopust, T.: Complexity in union-free regular languages. Int. J. Found. Comput. Sci. 22(7), 1639–1653 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Jirásková, G., Mlynárčik, P.: Complement on prefix-free, suffix-free, and non-returning NFA languages. In: Jürgensen, H., Karhumäki, J., Okhotin, A. (eds.) DCFS 2014. LNCS, vol. 8614, pp. 222–233. Springer, Heidelberg (2014)Google Scholar
  13. 13.
    Glaister, I., Shallit, J.: A lower bound technique for the size of nondeterministic finite automata. Inform. Process. Lett. 59, 75–77 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Mlynárčik, P.: Complement on free and ideal languages. In: Shallit, J., Okhotin, A. (eds.) DCFS 2015. LNCS, vol. 9118, pp. 185–196. Springer, Heidelberg (2015)CrossRefGoogle Scholar
  15. 15.
    Sipser, M.: Introduction to the Theory of Computation. PWS Publishing Company, Boston (1997)zbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Michal Hospodár
    • 1
  • Galina Jirásková
    • 1
  • Peter Mlynárčik
    • 1
  1. 1.Mathematical Institute, Slovak Academy of SciencesKošiceSlovakia

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