{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T22:02:08Z","timestamp":1649109728706},"reference-count":9,"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":[[2006,6]]},"abstract":"<jats:p> Let [Formula: see text] be a class of semigroups containing all finite commutative bands, and let p(x) be a real polynomial. The [Formula: see text]-completion problem asks whether for a given partial groupoid G there exists a semigroup [Formula: see text] such that G \u2286 S, every product for (a, b) \u2208 G<jats:sup>2<\/jats:sup> defined in G coincides with that for (a, b) in S, and |S| \u2264 p(|G|). We prove the problem to be \u2115\u2119-hard in general and \u2115\u2119-complete if the membership problem for [Formula: see text] is in \u2119. <\/jats:p>","DOI":"10.1142\/s0218196706003086","type":"journal-article","created":{"date-parts":[[2006,7,10]],"date-time":"2006-07-10T03:00:12Z","timestamp":1152500412000},"page":"551-562","source":"Crossref","is-referenced-by-count":1,"title":["ON COMPLETING PARTIAL GROUPOIDS TO SEMIGROUPS"],"prefix":"10.1142","volume":"16","author":[{"given":"P.","family":"GORAL\u010c\u00cdK","sequence":"first","affiliation":[{"name":"LIFAR, Facult\u00e9 des Sciences et des Techniques, Universit\u00e9 de Rouen, Pl. E. Blondel, 76821 Mont Saint Aignan Cedex, France"}]},{"given":"V.","family":"KOUBEK","sequence":"additional","affiliation":[{"name":"Department of Theoretical Computer Science, Faculty of Mathematics and Physics, Charles University, Malostransk\u00e9 n\u00e1m. 25, 118 00 Praha 1, Czech Republic"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-75357-2"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1137\/0206023"},{"key":"rf3","volume-title":"The Algebraic Theory of Semigroups","author":"Clifford A. H.","year":"1968"},{"key":"rf4","volume-title":"Universal Algebra","author":"Cohn P. M.","year":"1965"},{"key":"rf5","first-page":"64","volume":"26","author":"Evans T.","journal-title":"J. London Math. Soc."},{"key":"rf6","volume-title":"Computers and Intractability, A Guide to the Theory of NP-Completeness","author":"Garey M. R.","year":"1979"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-4049(96)00050-3"},{"key":"rf8","volume-title":"Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations","author":"Magnus W.","year":"1976"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1999.8138"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196706003086","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T22:28:01Z","timestamp":1565130481000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196706003086"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,6]]},"references-count":9,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2006,6]]}},"alternative-id":["10.1142\/S0218196706003086"],"URL":"https:\/\/doi.org\/10.1142\/s0218196706003086","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,6]]}}}