{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,21]],"date-time":"2026-09-21T05:01:47Z","timestamp":1789966907080,"version":"4.0.1"},"reference-count":6,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Comput."],"published-print":{"date-parts":[[1979,8]]},"abstract":"<jats:p>We study the average-case complexity of finding all occurrences of a given pattern $\\alpha $ in an input text string. Over an alphabet of q symbols, let $c(\\alpha ,n)$ be the minimum average number of characters that need to be examined in a random text string of length n. We prove that, for large m, almost all patterns $\\alpha $ of length m satisfy \\[ c(\\alpha ,n) = \\theta \\left( \\left\\lceil \\log _q \\left(\\frac{{n - m}}{{\\ln m}} + 2\\right) \\right\\rceil \\right)\\quad \\text{if }m \\leqq n \\leqq 2m, \\] and \\[ c(\\alpha ,n) = \\theta \\left( \\frac{{\\lceil {\\log _q m} \\rceil }}{m}n \\right)\\quad{\\text{if }} n &gt; 2m. \\] This in particular confirms a conjecture raised in a recent paper by Knuth, Morris, and Pratt (Fast pattern matching in strings, SIAM J. Comput., 6 (1977), pp. 323\u2013350.<\/jats:p>","DOI":"10.1137\/0208029","type":"journal-article","created":{"date-parts":[[2005,2,24]],"date-time":"2005-02-24T06:03:31Z","timestamp":1109225011000},"page":"368-387","source":"Crossref","is-referenced-by-count":99,"title":["The Complexity of Pattern Matching for a Random String"],"prefix":"10.1137","volume":"8","author":[{"given":"Andrew Chi-Chih","family":"Yao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,13]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1145\/360825.360855"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1145\/321921.321922"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1145\/359842.359859"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/0206024"},{"key":"R5","volume-title":"The art of computer programming. Volume 3","author":"Knuth Donald E.","year":"1973"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/0206048"}],"container-title":["SIAM Journal on Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/0208029","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:34:08Z","timestamp":1787337248000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/0208029"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1979,8]]},"references-count":6,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1979,8]]}},"alternative-id":["10.1137\/0208029"],"URL":"https:\/\/doi.org\/10.1137\/0208029","relation":{},"ISSN":["0097-5397","1095-7111"],"issn-type":[{"value":"0097-5397","type":"print"},{"value":"1095-7111","type":"electronic"}],"subject":[],"published":{"date-parts":[[1979,8]]}}}