Skip to main content
SpringerLink
Log in

Syntactic Complexities of Some Classes of Star-Free Languages

  • Conference paper
Descriptional Complexity of Formal Systems (DCFS 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7386))

Included in the following conference series:

Abstract

The syntactic complexity of a regular language is the cardinality of its syntactic semigroup. The syntactic complexity of a subclass of regular languages is the maximal syntactic complexity of languages in that subclass, taken as a function of the state complexity n of these languages. We study the syntactic complexity of three subclasses of star-free languages. We find tight upper bounds for languages accepted by monotonic, partially monotonic and “nearly monotonic” automata; all three of these classes are star-free. We conjecture that the bound for nearly monotonic languages is also a tight upper bound for star-free languages.

This work was supported by the Natural Sciences and Engineering Research Council of Canada under grant No. OGP0000871.

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. Ananichev, D.S., Volkov, M.V.: Synchronizing generalized monotonic automata. Theoret. Comput. Sci. 330(1), 3–13 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  2. Brzozowski, J.: Quotient complexity of regular languages. J. Autom. Lang. Comb. 15(1/2), 71–89 (2010)

    Google Scholar 

  3. Brzozowski, J., Li, B., Ye, Y.: Syntactic complexity of prefix-, suffix-, bifix-, and factor-free regular languages. Theoret. Comput. Sci. (in press, 2012)

    Google Scholar 

  4. Brzozowski, J., Liu, B.: Quotient complexity of star-free languages. In: Dömösi, P., Szabolcs, I. (eds.) 13th International Conference on Automata and Formal Languages (AFL), pp. 138–152. Institute of Mathematics and Informatics, College of Nyíregyháza (2011)

    Google Scholar 

  5. Brzozowski, J., Ye, Y.: Syntactic Complexity of Ideal and Closed Languages. In: Mauri, G., Leporati, A. (eds.) DLT 2011. LNCS, vol. 6795, pp. 117–128. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  6. Caley, A.: A theorem on trees. Quart. J. Math. 23, 376–378 (1889)

    Google Scholar 

  7. GAP-Group: GAP - Groups, Algorithms, Programming - a System for Computational Discrete Algebra (2010), http://www.gap-system.org/

  8. Gomes, G., Howie, J.: On the ranks of certain semigroups of order-preserving transformations. Semigroup Forum 45, 272–282 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  9. Holzer, M., König, B.: On deterministic finite automata and syntactic monoid size. Theoret. Comput. Sci. 327(3), 319–347 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  10. Holzer, M., Kutrib, M., Meckel, K.: Nondeterministic state complexity of star-free languages. Theoret. Comput. Sci. (in press, 2012)

    Google Scholar 

  11. Howie, J.M.: Products of idempotents in certain semigroups of transformations. Proc. Edinburgh Math. Soc. 17(2), 223–236 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  12. Krawetz, B., Lawrence, J., Shallit, J.: State complexity and the monoid of transformations of a finite set (2003), http://arxiv.org/abs/math/0306416v1

  13. Laradji, A., Umar, A.: Asymptotic results for semigroups of order-preserving partial transformations. Comm. Alg. 34(3), 1071–1075 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  14. Maslov, A.N.: Estimates of the number of states of finite automata. Dokl. Akad. Nauk SSSR 194, 1266–1268 (1970) (Russian); english translation: Soviet Math. Dokl. 11, 1373–1375 (1970)

    MathSciNet  Google Scholar 

  15. McNaughton, R., Papert, S.A.: Counter-Free Automata. M.I.T. research monograph, vol. 65. The MIT Press (1971)

    Google Scholar 

  16. Myhill, J.: Finite automata and the representation of events. Wright Air Development Center Technical Report 57–624 (1957)

    Google Scholar 

  17. Nerode, A.: Linear automaton transformations. Proc. Amer. Math. Soc. 9, 541–544 (1958)

    Article  MathSciNet  MATH  Google Scholar 

  18. Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages, vol. 1: Word, Language, Grammar. Springer, New York (1997)

    MATH  Google Scholar 

  19. Schützenberger, M.P.: On finite monoids having only trivial subgroups. Inform. and Control 8, 190–194 (1965)

    Article  MATH  Google Scholar 

  20. Shor, P.W.: A new proof of Cayley’s formula for counting labeled trees. J. Combin. Theory Ser. A 71(1), 154–158 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  21. Yu, S.: State complexity of regular languages. J. Autom. Lang. Comb. 6, 221–234 (2001)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, Canada, N2L 3G1

    Janusz Brzozowski & Baiyu Li

Authors
  1. Janusz Brzozowski
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Baiyu Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut für Informatik, Universität Giessen, Arndtstraße 2, 35392, Giessen, Germany

    Martin Kutrib

  2. Departamento de Ciência de Computadores, Universidade do Porto, Faculdade de Ciências, Rua do Campo Alegre 1021-1055, 4169-007, Porto, Portugal

    Nelma Moreira  & Rogério Reis  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Brzozowski, J., Li, B. (2012). Syntactic Complexities of Some Classes of Star-Free Languages. In: Kutrib, M., Moreira, N., Reis, R. (eds) Descriptional Complexity of Formal Systems. DCFS 2012. Lecture Notes in Computer Science, vol 7386. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31623-4_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-31623-4_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31622-7

  • Online ISBN: 978-3-642-31623-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation