Open AccessDynamic Algorithms for the Dyck Languages
Author(s) -
Gudmund Skovbjerg Frandsen,
Thore Husfeldt,
Peter Bro Miltersen,
Theis Rauhe,
Søren Skyum
Publication year - 1995
Publication title -
brics report series
Language(s) - English
Resource type - Journals
eISSN - 1601-5355
pISSN - 0909-0878
DOI - 10.7146/brics.v2i1.19503
Subject(s) - las vegas , computer science , string (physics) , algorithm , word (group theory) , class (philosophy) , time complexity , theoretical computer science , combinatorics , mathematics , artificial intelligence , medicine , geometry , metropolitan area , pathology , mathematical physics
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.