{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,2,27]],"date-time":"2024-02-27T21:14:48Z","timestamp":1709068488898},"reference-count":10,"publisher":"World Scientific Pub Co Pte Lt","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2010,12]]},"abstract":"<jats:p> We study the computational complexity of the satisfiability problem of an equation between terms over a finite algebra (TERM-SAT). We describe many classes of algebras where the complexity of TERM-SAT is determined by the clone of term operations. We classify the complexity for algebras generating maximal clones. Using this classification we describe many of algebras where TERM-SAT is NP-complete. We classify the situation for clones which are generated by an order or a permutation relation. We introduce the concept of semiaffine algebras and show polynomial-time algorithms which solve the satisfiability problem for them. <\/jats:p>","DOI":"10.1142\/s021819671000600x","type":"journal-article","created":{"date-parts":[[2010,12,28]],"date-time":"2010-12-28T05:27:42Z","timestamp":1293514062000},"page":"1001-1020","source":"Crossref","is-referenced-by-count":4,"title":["TERM EQUATION SATISFIABILITY OVER FINITE ALGEBRAS"],"prefix":"10.1142","volume":"20","author":[{"given":"TOMASZ A.","family":"GORAZD","sequence":"first","affiliation":[{"name":"Algorithmics Research Group, Jagiellonian University, ul. \u0141ojasiewicza 6, 30-348 Krak\u00f3w, Poland"}]},{"given":"JACEK","family":"KRZACZKOWSKI","sequence":"additional","affiliation":[{"name":"Institute of Computer Science, Maria Curie-Sk\u0142odowska University, pl. M.Curie-Sk\u0142odowskiej 1, 20-031 Lublin, Poland"}]}],"member":"219","published-online":{"date-parts":[[2012,4,30]]},"reference":[{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539794266766"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/S0890-5401(02)93173-1"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196706003256"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(97)00230-2"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196706003116"},{"key":"rf11","series-title":"Annals of Mathematics Studies","volume-title":"The Two-valued Iterative Systems of Mathematical Logic","volume":"5","author":"Post E.","year":"1941"},{"key":"rf12","first-page":"3","volume":"80","author":"Rosenberg I. G.","journal-title":"Rozpravy Ceskoslovensk\u00e9 Akad. v\u011bd, Ser. Math. Nat. Sci"},{"key":"rf13","volume-title":"Computational Complexity","author":"Papadimitrou Ch. H.","year":"1994"},{"key":"rf14","first-page":"603","volume":"28","author":"Quackenbush R. W.","journal-title":"Colloquia Mathematica Societatis Jnos Bolyai"},{"key":"rf17","first-page":"44","volume":"127","author":"Yanov Yu. I.","journal-title":"Dokl. Akad. Nauk SSSR"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021819671000600X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T23:31:57Z","timestamp":1565134317000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S021819671000600X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,12]]},"references-count":10,"journal-issue":{"issue":"08","published-online":{"date-parts":[[2012,4,30]]},"published-print":{"date-parts":[[2010,12]]}},"alternative-id":["10.1142\/S021819671000600X"],"URL":"https:\/\/doi.org\/10.1142\/s021819671000600x","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,12]]}}}