{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T16:19:41Z","timestamp":1777133981781,"version":"3.51.4"},"reference-count":8,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2012,10,30]],"date-time":"2012-10-30T00:00:00Z","timestamp":1351555200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Theory and Practice of Logic Programming"],"published-print":{"date-parts":[[2014,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The rules of Sudoku are often specified using 27 <jats:monospace>all_different<\/jats:monospace> constraints, referred to as the <jats:italic>big<\/jats:italic> constraints. Using graphical proofs and exploratory logic programming, the following main and new result is obtained: Many subsets of six of these big constraints are redundant (i.e., they are entailed by the remaining 21 constraints), and six is maximal (i.e., removing more than six constraints is not possible while maintaining equivalence). The corresponding result for binary inequality constraints, referred to as the <jats:italic>small<\/jats:italic> constraints, is stated as a conjecture.<\/jats:p>","DOI":"10.1017\/s1471068412000361","type":"journal-article","created":{"date-parts":[[2012,10,30]],"date-time":"2012-10-30T09:25:53Z","timestamp":1351589153000},"page":"363-377","source":"Crossref","is-referenced-by-count":3,"title":["Redundant Sudoku rules"],"prefix":"10.1017","volume":"14","author":[{"given":"BART","family":"DEMOEN","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"MARIA","family":"GARCIA DE LA BANDA","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2012,10,30]]},"reference":[{"key":"S1471068412000361_ref3","volume-title":"A to Z of SUDOKU","author":"Jussien","year":"2007"},{"key":"S1471068412000361_ref5","unstructured":"McGuire G. , Tugemann B. and Civario G. 2012. There is no 16-clue Sudoku: Solving the Sudoku minimum number of clues problem. CoRR abs\/1201.0749."},{"key":"S1471068412000361_ref2","volume-title":"Proceedings of the 9th International Symposium on Artificial Intelligence and Mathematics (AIMATH 2006)","author":"Ist","year":"2006"},{"key":"S1471068412000361_ref7","unstructured":"Royle G. Minimum Sudoku. Accessed September 2012. URL: http:\/\/school.maths.uwa.edu.au\/\u223cgordon\/sudokumin.php."},{"key":"S1471068412000361_ref4","unstructured":"Kwon G. and Jain H. 2006. Optimized CNF encoding for Sudoku puzzles. In Short paper presentation at the 13th International Conference on Logic for Programming Artificial Intelligence and Reasoning (LPAR 2006)."},{"key":"S1471068412000361_ref1","unstructured":"Demoen B. and Garcia de la Banda M. 2012. Maximal Sets of Redundant Constraints in Latin Square. Monash University, no. 2012\/269. Technical Report."},{"key":"S1471068412000361_ref8","unstructured":"Wikipedia. n.d. Sudoku. Accessed September 2012. URL: http:\/\/en.wikipedia.org\/wiki\/Sudoku."},{"key":"S1471068412000361_ref6","doi-asserted-by":"publisher","DOI":"10.1017\/S1471068412000130"}],"container-title":["Theory and Practice of Logic Programming"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1471068412000361","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,22]],"date-time":"2019-04-22T16:31:20Z","timestamp":1555950680000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1471068412000361\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,10,30]]},"references-count":8,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2014,5]]}},"alternative-id":["S1471068412000361"],"URL":"https:\/\/doi.org\/10.1017\/s1471068412000361","relation":{},"ISSN":["1471-0684","1475-3081"],"issn-type":[{"value":"1471-0684","type":"print"},{"value":"1475-3081","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,10,30]]}}}