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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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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