Skip to main content

Nondeterministic Complexity of Operations on Closed and Ideal Languages

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9705))

Abstract

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.

P. Mlynárčik—Research supported by VEGA grant 2/0084/15.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Birget, J.C.: Partial orders on words, minimal elements of regular languages, and state complexity. Theoret. Comput. Sci. 119, 267–291 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  2. Brzozowski, J., Jirásková, G., Li, B.: Quotient complexity of ideal languages. Theoret. Comput. Sci. 470, 36–52 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  3. Brzozowski, J., Jirásková, G., Zou, C.: Quotient complexity of closed languages. Theor. Comput. Syst. 54, 277–292 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. Han, Y.-S., Salomaa, K.: Nondeterministic state complexity for suffix-free regular languages. In: DCFS 2010, pp. 189–196 (2010)

    Google Scholar 

  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)

    MathSciNet  MATH  Google Scholar 

  8. Holzer, M., Kutrib, M.: Nondeterministic descriptional complexity of regular languages. Int. J. Found. Comput. Sci. 14, 1087–1102 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  9. Jirásková, G.: State complexity of some operations on binary regular languages. Theoret. Comput. Sci. 330, 287–298 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  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. Jirásková, G., Masopust, T.: Complexity in union-free regular languages. Int. J. Found. Comput. Sci. 22(7), 1639–1653 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  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. Glaister, I., Shallit, J.: A lower bound technique for the size of nondeterministic finite automata. Inform. Process. Lett. 59, 75–77 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  15. Sipser, M.: Introduction to the Theory of Computation. PWS Publishing Company, Boston (1997)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Galina Jirásková .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Hospodár, M., Jirásková, G., Mlynárčik, P. (2016). Nondeterministic Complexity of Operations on Closed and Ideal Languages. In: Han, YS., Salomaa, K. (eds) Implementation and Application of Automata. CIAA 2016. Lecture Notes in Computer Science(), vol 9705. Springer, Cham. https://doi.org/10.1007/978-3-319-40946-7_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-40946-7_11

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40945-0

  • Online ISBN: 978-3-319-40946-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics