Skip to main content
SpringerLink
Log in

Descriptional Complexity of Operations on Alternating and Boolean Automata

  • Conference paper
Book cover Computer Science – Theory and Applications (CSR 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7353))

Included in the following conference series:

Abstract

The paper shows that the tight bound for the conversion of alternating finite automata into nondeterministic finite automata with a single initial state is 2n + 1. This solves an open problem stated by Fellah et al. (Intern. J. Computer Math. 35, 1990, 117–132). Then we examine the complexity of basic operations on languages represented by boolean and alternating finite automata. We get tight bounds for intersection and union, and for concatenation and reversal of languages represented by boolean automata. In the case of star, and of concatenation and reversal of AFA languages, our upper and lower bounds differ by one.

Research supported by VEGA grant 2/0183/11.

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

Access this chapter

Log in via an institution
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 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Brzozowski, J., Leiss, E.: On equations for regular languages, finite automata, and sequential networks. Theoret. Comput. Sci. 10, 19–35 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  2. Chandra, A.K., Kozen, D.C., Stockmeyer, L.J.: Alternation. JACM 28, 114–133 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  3. Fellah, A., Jürgensen, H., Yu, S.: Constructions for alternating finite automata. Intern. J. Computer Math. 35, 117–132 (1990)

    Article  MATH  Google Scholar 

  4. Jirásek, J., Jirásková, G., Szabari, A.: State complexity of concatenation and complementation. Internat. J. Found. Comput. Sci. 16, 511–529 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  5. Jirásková, G., Masopust, T.: Complexity in Union-Free Regular Languages. In: Gao, Y., Lu, H., Seki, S., Yu, S. (eds.) DLT 2010. LNCS, vol. 6224, pp. 255–266. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  6. Jirásková, G., Masopust, T.: State Complexity of Projected Languages. In: Holzer, M., Kutrib, M., Pighizzini, G. (eds.) DCFS 2011. LNCS, vol. 6808, pp. 198–211. Springer, Heidelberg (2011)

    Google Scholar 

  7. Jirásková, G., Šebej, J.: Note on Reversal of Binary Regular Languages. In: Holzer, M., Kutrib, M., Pighizzini, G. (eds.) DCFS 2011. LNCS, vol. 6808, pp. 212–221. Springer, Heidelberg (2011)

    Google Scholar 

  8. Kozen, D.: On parallelism in turing machines. In: Proc. 17th FOCS, pp. 89–97 (1976)

    Google Scholar 

  9. Leiss, E.: Succinct representation of regular languages by boolean automata. Theoret. Comput. Sci. 13, 323–330 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  10. Leiss, E.: On generalized language equations. Theoret. Comput. Sci. 14, 63–77 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  11. Maslov, A.N.: Estimates of the number of states of finite automata. Soviet Math. Doklady 11, 1373–1375 (1970)

    MATH  Google Scholar 

  12. Sipser, M.: Introduction to the theory of computation. PWS Publishing Company, Boston (1997)

    MATH  Google Scholar 

  13. Yu, S.: Regular languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, ch. 2, vol. I, pp. 41–110. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  14. Yu, S., Zhuang, Q., Salomaa, K.: The state complexity of some basic operations on regular languages. Theoret. Comput. Sci. 125, 315–328 (1994)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, 040 01, Košice, Slovakia

    Galina Jirásková

Authors
  1. Galina Jirásková
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Steklov Institute of Mathematics at St.Petersburg, 191023, St. Petersburg, Russia

    Edward A. Hirsch

  2. University of Turku, 20014, Turku, Finland

    Juhani Karhumäki  & Arto Lepistö  & 

  3. Lobachevky State University of Nizhni Novgorod, 603950, Niszhi Novgorod, Russia

    Michail Prilutskii

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Jirásková, G. (2012). Descriptional Complexity of Operations on Alternating and Boolean Automata. In: Hirsch, E.A., Karhumäki, J., Lepistö, A., Prilutskii, M. (eds) Computer Science – Theory and Applications. CSR 2012. Lecture Notes in Computer Science, vol 7353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30642-6_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-30642-6_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30641-9

  • Online ISBN: 978-3-642-30642-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation