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Dynamic algorithms for the Dyck languages

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Algorithms and Data Structures (WADS 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 955))

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Abstract

We study Dynamic Membership problems for the Dyck languages, the class of strings of properly balanced parentheses. We also study the Dynamic Word problem for the free group. We present deterministic algorithms and data structures which maintain a string under replacements of symbols, insertions, and deletions of symbols, and language membership queries. Updates and queries are handled in polylogarithmic time. We also give both Las Vegas- and Monte Carlo-type randomised algorithms to achieve better running times, and present lower bounds on the complexity for variants of the problems.

A full version of this paper with all proofs included, can be found on the BRICS World Wide Web server at URL http://www.daimi.aau.dk/BRICS/. This work was partially supported by the ESPRIT II Basic Research Actions Program of the EC under contract no. 7141 (project ALCOM II).

Gudmund Frandsen was partially supported by CCI-Europe.

Peter Bro Miltersen was partially supported by a grant from the Danish Natural Science Research Council, part of his research was done done at the Department of Computer Science, University of Toronto,

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References

  1. Paul F. Dietz. Optimal algorithms for list indexing and subset rank. In F. Dehne, J.-R. Sack, and N. Santoro, editors, Proc. First Workshop on Algorithms and Data Structures (WADS), volume 382 of Lecture Notes in Computer Science, pages 39–46. Springer Verlag, Berlin, 1989.

    Google Scholar 

  2. Gudmund Skovbjerg Frandsen, Peter Bro Miltersen, and Sven Skyum. Dynamic word problems. In Proc 34th Ann. Symp. on Foundations of Computer Science (FOCS), pages 470–479, 1993.

    Google Scholar 

  3. Michael L. Fredman. The complexity of maintaining an array and computing its partial sums. Journal of the ACM, 29:250–260, 1982.

    Article  Google Scholar 

  4. Michael L. Fredman and Michael E. Saks. The cell probe complexity of dynamic data structures. In Proc. 21st Ann. Symp. on Theory of Computing (STOC), pages 345–354, 1989.

    Google Scholar 

  5. Leo J. Guibas and Robert Sedgewick. A dichromatic framework for balanced trees. In Proc. 19th Ann. Symp. on Foundations of Computer Science (FOCS), pages 8–21. IEEE Computer Society, 1978.

    Google Scholar 

  6. Michael A. Harrison. Introduction to Formal Language Theory. Addison-Wesley, 1978.

    Google Scholar 

  7. Richard M. Karp and Michael O. Rabin. Efficient randomised pattern-matching algorithms. IBM J. Res. Develop., 31(2):249–260, March 1987.

    Google Scholar 

  8. Richard J. Lipton and Yechezkel Zalcstein. Word problems solvable in logspace. Journal of the ACM, 24(3):522–526, 1977.

    Article  Google Scholar 

  9. Wilhelm Magnus, Abraham Karrass, and Donald Solitar. Combinatorial Group Theory, volume 13 of Pure and Applied Mathematics. Interscience Publishers, 1966.

    Google Scholar 

  10. K. Mehlhorn, R. Sundar, and C. Uhrig. Maintaining dynamic sequences under equality-tests in polylogarithmic time. In Proc. 5th Ann. Symp. on Discrete Algorithms (SODA), pages 213–222. ACM-SIAM, 1994.

    Google Scholar 

  11. Peter Bro Miltersen. Lower bounds for union-split-find related problems on random access machines. In Proc. 26th Ann. Symp. on Theory of Computing (STOC), pages 625–634. ACM, 1994.

    Google Scholar 

  12. Mark H. Overmars. The design of dynamic data structures, volume 156 of Lecture Notes in Computer Science. Springer Verlag, Berlin, 1983.

    Google Scholar 

  13. Sushant Patnaik and Neil Immerman. Dyn-FO: A parallel, dynamic comlexity class. In Proc. 13th ACM Symp. on Principles of Database Systems (PODS), pages 210–221, 1994.

    Google Scholar 

  14. R. W. Ritchie and F. N. Springsteel. Language recognition by marking automata. Information and Control, 20:313–330, 1972.

    Article  Google Scholar 

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Authors and Affiliations

  1. Basic Research in Computer Science, Centre of the Danish National Research Foundation, Department of Computer Science, University of Aarhus, Ny Munkegade, DK-8000, Århus C, Denmark

    Gudmund Skovbjerg Frandsen, Thore Husfeldt, Peter Bro Miltersen, Theis Rauhe & Søren Skyum

Authors
  1. Gudmund Skovbjerg Frandsen
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  2. Thore Husfeldt
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  3. Peter Bro Miltersen
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  4. Theis Rauhe
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  5. Søren Skyum
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Editor information

Selim G. Akl Frank Dehne Jörg-Rüdiger Sack Nicola Santoro

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© 1995 Springer-Verlag Berlin Heidelberg

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Frandsen, G.S., Husfeldt, T., Miltersen, P.B., Rauhe, T., Skyum, S. (1995). Dynamic algorithms for the Dyck languages. In: Akl, S.G., Dehne, F., Sack, JR., Santoro, N. (eds) Algorithms and Data Structures. WADS 1995. Lecture Notes in Computer Science, vol 955. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60220-8_54

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  • DOI: https://doi.org/10.1007/3-540-60220-8_54

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60220-0

  • Online ISBN: 978-3-540-44747-4

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