{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T10:35:35Z","timestamp":1648895735072},"reference-count":6,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[1999,2]]},"abstract":"<jats:p> A locally testable semigroup S is a semigroup with the property that for some non-negative integer k, called the order or level of local testability, two words u and v in some set of generators for S are equal in the semigroup if (1) the prefix and suffix of the words of length k coincide, and (2) the set of intermediate substrings of length k of the words coincide. The local testability problem for semigroups is, given a finite semigroup, to decide, if the semigroup is locally testable or not. <\/jats:p><jats:p> Recently, we introduced a polynomial time algorithm for the local testability problem and to find the level of local testability for semigroups based on our previous description of identities of k-testable semigroups and the structure of locally testable semigroups. <\/jats:p><jats:p> The first part of the algorithm we introduce solves the local testability problem. <\/jats:p><jats:p> The second part of the algorithm finds the order of local testability of a semigroup. The algorithm is of order n<jats:sup>2<\/jats:sup>, where n is the order of the semigroup. <\/jats:p>","DOI":"10.1142\/s0218196799000035","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T07:05:54Z","timestamp":1027753554000},"page":"31-39","source":"Crossref","is-referenced-by-count":7,"title":["A POLYNOMIAL TIME ALGORITHM FOR LOCAL TESTABILITY AND ITS LEVEL"],"prefix":"10.1142","volume":"09","author":[{"given":"A. N.","family":"TRAHTMAN","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Science, Bar-Ilan University, 52900 Ramat Gan, Israel"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(73)80005-6"},{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-51859-2_7"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1109\/12.93741"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1007\/BF02572744"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1007\/BF02573687"},{"key":"p_8","first-page":"151","volume":"5","author":"Zalcstein Y.","year":"1973","journal-title":"Semigroup Forum"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196799000035","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T17:54:38Z","timestamp":1565114078000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196799000035"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,2]]},"references-count":6,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[1999,2]]}},"alternative-id":["10.1142\/S0218196799000035"],"URL":"https:\/\/doi.org\/10.1142\/s0218196799000035","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,2]]}}}