Skip to main content
SpringerLink
Log in

Fast enumeration of words generated by Dyck grammars

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

The problem of enumerating and denumerating words generated by Dyck grammars arises in the work of compilers for high-level programming languages and a number of other applications. The present paper proposes an algorithm for the fast enumeration and denumeration of words of Dyck languages; the complexity of this algorithm per one symbol of enumerated words is O(log3 n log log n) bit operations, provided that the Schönhage-Strassen multiplication and division algorithmis used. The well-knownmethods applied earlier possess complexityO(n) per one symbol of enumerated words. The construction of the proposed algorithm is based on the Ryabko method.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. T. J. Lunch, “Sequence time coding for data compression,” Proc. IEEE 54(10), 1490–1491 (1966).

    Article  Google Scholar 

  2. Yu. S. Medvedeva and B. Ya. Ryabko, “A fast algorithm for the enumeration of words with given constraints on the run lengths of ones,” Problemy Peredachi Informatsii 46(4), 130–139 (2010) [Probl. Inform. Transm. 46 (4), 390–399 (2010)].

    MathSciNet  Google Scholar 

  3. T.M. Cover, “Enumerative Source Encoding,” IEEE Trans. Information Theory IT-19(1), 73–77 (1973).

    Article  MathSciNet  Google Scholar 

  4. B. Ya. Ryabko, “Fast enumeration of combinatorial objects,” Diskret. Mat. 10(2), 101–119 (1998) [Discrete Math. Appl. 8 (2), 163–182 (1998)].

    Article  MathSciNet  Google Scholar 

  5. A. E. Pentus and M. R. Pentus, Theory of Formal Languages, A manual (Izd. TsPI, Mekh.-Mat. Moskov. Univ., Moscow, 2004) [in Russian].

    Google Scholar 

  6. E. Reingold, J. Nievergelt, and N. Deo, Combinatorial Algorithms: Theory and Practice (Prentice-Hall, Englewood Cliffs, NJ, 1977; Mir, Moscow, 1980). Compilers: Principles, Techniques, and Tools[1] is a computer science textbook by Alfred V. Aho, Monica S. Lam, Ravi Sethi, and Jeffrey D. Ullman about compiler construction

    Google Scholar 

  7. A. V. Aho, M. S. Lam, R. Sethi, and J. D. Ullman, Compilers: Principles, Techniques, and Tools (Pearson Education, Inc., 2006; Williams, Moscow, 2008).

    Google Scholar 

  8. R. E. Krichevskii, Information Compression and Search (Radio i Svyaz, Moscow, 1989) [in Russian].

    Google Scholar 

  9. A. Schönhage and V. Strassen, “Schnelle Multiplikation grosser Zahlen,” Computing 7(3–4), 281–292 (1971).

    Article  MATH  Google Scholar 

  10. M. Fürer, “Faster integer multiplication,” in Proceedings of the 39th Annual ACM Symposium on Theory of Computing (ACM, New York, 2007), pp. 57–66.

    Google Scholar 

  11. A. Shen’, Programming: Theorems and Problems (MTsNMO, Moscow, 2004) [in Russian].

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Computational Technologies, Russian Academy of Sciences, Novosibirsk, Russia

    Yu. S. Medvedeva

Authors
  1. Yu. S. Medvedeva
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yu. S. Medvedeva.

Additional information

Original Russian Text © Yu. S. Medvedeva, 2014, published in Matematicheskie Zametki, 2014, Vol. 96, No. 1, pp. 51–69.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Medvedeva, Y.S. Fast enumeration of words generated by Dyck grammars. Math Notes 96, 68–83 (2014). https://doi.org/10.1134/S0001434614070062

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0001434614070062

Keywords

Search

Navigation