{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,3,20]],"date-time":"2024-03-20T11:01:17Z","timestamp":1710932477529},"reference-count":13,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2003,6]]},"abstract":"<jats:p> A mapping \u03d5:\u2124 \u2192 \u2124 is called piecewise affine if there exist integers a\u2265 1 and u<jats:sub>j<\/jats:sub>\u2265 1, v<jats:sub>j<\/jats:sub> for 0\u2264 j&lt;a such that \u03d5(an+j)=u<jats:sub>j<\/jats:sub>n+v<jats:sub>j<\/jats:sub> whenever n\u2208 \u2124 and 0\u2264 j&lt;a. We prove that if s=(s(n))<jats:sub>n\u2265 0<\/jats:sub> and t=(t(n))<jats:sub>n\u2265 0<\/jats:sub> are \u2115-rational sequences such that s takes each value exactly as many times as t, then there exists a piecewise affine mapping \u03d5:\u2124 \u2192 \u2124 such that s(n)=t(\u03d5(n)) for almost all n\u2265 0. As an application we solve the HD0L language equivalence problem in some cases. <\/jats:p>","DOI":"10.1142\/s0218196703001390","type":"journal-article","created":{"date-parts":[[2003,8,20]],"date-time":"2003-08-20T05:30:13Z","timestamp":1061357413000},"page":"303-321","source":"Crossref","is-referenced-by-count":4,"title":["On the Images of \u2115-Rational Sequences Counting Multiplicities"],"prefix":"10.1142","volume":"13","author":[{"given":"Juha","family":"Honkala","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Turku, 20014 Turku, Finland"}]},{"given":"Keijo","family":"Ruohonen","sequence":"additional","affiliation":[{"name":"Department of Mathematics,  Tampere University of Technology, 33101 Tampere, Finland"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","unstructured":"J.\u00a0Berstel and M.\u00a0Nielsen, Automata, Languages and Development, eds. A.\u00a0Lindenmayer and G.\u00a0Rozenberg (North-Holland, Amsterdam, 1976)\u00a0pp. 161\u2013178."},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-73235-5"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(86)90168-4"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(00)00158-4"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(01)00010-X"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-1779-2"},{"key":"rf7","volume-title":"The Mathematical Theory of L Systems","author":"Rozenberg G.","year":"1980"},{"key":"rf8","first-page":"369","volume":"4","author":"Ruohonen K.","journal-title":"Fund. Inf."},{"key":"rf9","unstructured":"K.\u00a0Ruohonen, The Book of L, eds. G.\u00a0Rozenberg and A.\u00a0Salomaa (Springer, Berlin, 1986)\u00a0pp. 394\u2013401."},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(85)90035-0"},{"key":"rf11","first-page":"135","volume":"38","author":"Ruohonen K.","journal-title":"Fund. Inf."},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-6264-0"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-1988-0929498-X"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196703001390","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T18:25:29Z","timestamp":1565115929000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196703001390"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,6]]},"references-count":13,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2003,6]]}},"alternative-id":["10.1142\/S0218196703001390"],"URL":"https:\/\/doi.org\/10.1142\/s0218196703001390","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,6]]}}}