{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,2,19]],"date-time":"2023-02-19T05:50:36Z","timestamp":1676785836495},"reference-count":23,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2004,2]]},"abstract":"<jats:p> With ideas from data compression and combinatorics on words, we introduce a complexity measure for words, called repetition complexity, which quantifies the amount of repetition in a word. The repetition complexity of w, R (w), is defined as the smallest amount of space needed to store w when reduced by repeatedly applying the following procedure: n consecutive occurrences uu\u2026u of the same subword u of w are stored as (u,n). The repetition complexity has interesting relations with well-known complexity measures, such as subword complexity, SUB , and Lempel-Ziv complexity, LZ . We have always R (w)\u2265 LZ (w) and could even be that the former is linear while the latter is only logarithmic; e.g., this happens for prefixes of certain infinite words obtained by iterated morphisms. An infinite word \u03b1 being ultimately periodic is equivalent to: (i) [Formula: see text], (ii) [Formula: see text], and (iii) [Formula: see text]. De Bruijn words, well known for their high subword complexity, are shown to have almost highest repetition complexity; the precise complexity remains open. R (w) can be computed in time [Formula: see text] and it is open, and probably very difficult, to find fast algorithms. <\/jats:p>","DOI":"10.1142\/s0129054104002297","type":"journal-article","created":{"date-parts":[[2004,3,18]],"date-time":"2004-03-18T12:03:47Z","timestamp":1079611427000},"page":"41-55","source":"Crossref","is-referenced-by-count":7,"title":["WORD COMPLEXITY AND REPETITIONS IN WORDS"],"prefix":"10.1142","volume":"15","author":[{"given":"LUCIAN","family":"ILIE","sequence":"first","affiliation":[{"name":"Department of Computer Science, University of Western Ontario, N6A 5B7, London, Ontario, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"SHENG","family":"YU","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Western Ontario, N6A 5B7, London, Ontario, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"KAIZHONG","family":"ZHANG","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Western Ontario, N6A 5B7, London, Ontario, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(83)90109-3"},{"key":"rf2","first-page":"758","volume":"49","author":"de Bruijn N. 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