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DLT 2005, LNCS 3572, pp. 36–56, 2005. c Springer-Verlag Berlin Heidelberg 2005 Central Sturmian Words: Recent Developments 37 c0 , c1 , . . , cn , . . be any sequence of integers such that c0 ≥ 0 and ci > 0 for i > 0. We deﬁne, inductively, the sequence of words (sn )n≥0 , where s0 = b, s1 = a, and sn+1 = scnn−1 sn−1 for n ≥ 1 . The sequence (sn )n≥0 converges to a limit s which is an inﬁnite standard Sturmian word. Any standard Sturmian word is obtained in this way. We shall denote by Stand the set of all the words sn , n ≥ 0 of any standard sequence (sn )n≥0 .
In W. Kuich, G. Rozenberg, A. ), Developments in Language Theory [Lect. Notes Comput. Sci. , 2002, 166–174. 6. D. S. Ananichev and I. V. Petrov. Quest for short synchronizing words and short collapsing words. WORDS. Proc. 4th Int. , Univ. of Turku, Turku, 2003, 411–418. 7. C. Bergman and G. Slutzki. Complexity of some problems concerning varieties and quasi-varieties of algebras. SIAM J. Comput. 30 (2000) 359–382. 8. S. Burris and J. Lawrence, Results on the equivalence problem for finite groups.
This result was later improved in  by the use of other techniques. Also in , an eﬃcient data structure for dynamic text indexing based on LCP is described. Here the goal is to maintain a dynamic string, subject to single character insertions, deletions and replacements, so that substring membership queries can be answered eﬃciently. An improvement of this data structure, which is again based on LCP, was later described in . Finally,  shows how to maintain a dictionary data structure under insertion and deletion of dictionary entries so that given a text string, all occurrences of each dictionary entry can be eﬃciently computed.