{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T18:52:20Z","timestamp":1784227940664,"version":"3.55.0"},"reference-count":0,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2010,4,1]],"date-time":"2010-04-01T00:00:00Z","timestamp":1270080000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Fundamenta Informaticae"],"published-print":{"date-parts":[[2010,4]]},"abstract":"<jats:p>It is proved that the set of scattered substrings of a language recognized by an n-state DFA requires a DFA with at least 2 $^{n\/2-2}$ states (the known upper bound is 2 $^n$ ), with witness languages given over an exponentially growing alphabet. For a 3-letter alphabet, scattered substrings are shown to require at least 2 $^{sqrt{2n+30}-6}$ states. A similar state complexity function for scattered superstrings is determined to be exactly 2 $^{n-2}$ + 1 for an alphabet of at least n \u2212 2 letters, and strictly less for any smaller alphabet. For a 3-letter alphabet, the state complexity of scattered superstrings is at least 1\/5 4sqrt{n\/2}n-3\/4.<\/jats:p>","DOI":"10.3233\/fi-2010-252","type":"journal-article","created":{"date-parts":[[2019,12,2]],"date-time":"2019-12-02T23:29:33Z","timestamp":1575329373000},"page":"325-338","source":"Crossref","is-referenced-by-count":17,"title":["On the State Complexity of Scattered Substrings and Superstrings"],"prefix":"10.1177","volume":"99","author":[{"given":"Alexander","family":"Okhotin","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Turku Turku\r\t\t\t FIN\u00a8C20014, Finland, and Academy of Finland. E-mail: alexander.okhotin@utu.fi"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2010,4,1]]},"container-title":["Fundamenta Informaticae"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2010-252","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2010-252","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T06:32:32Z","timestamp":1777444352000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/FI-2010-252"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,4]]},"references-count":0,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2010,4]]}},"alternative-id":["10.3233\/FI-2010-252"],"URL":"https:\/\/doi.org\/10.3233\/fi-2010-252","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"value":"0169-2968","type":"print"},{"value":"1875-8681","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,4]]}}}