{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T18:51:30Z","timestamp":1725907890523},"publisher-location":"Berlin, Heidelberg","reference-count":17,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783662557501"},{"type":"electronic","value":"9783662557518"}],"license":[{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017]]},"DOI":"10.1007\/978-3-662-55751-8_11","type":"book-chapter","created":{"date-parts":[[2017,8,15]],"date-time":"2017-08-15T11:32:49Z","timestamp":1502796769000},"page":"123-135","source":"Crossref","is-referenced-by-count":1,"title":["Strong Duality in Horn Minimization"],"prefix":"10.1007","author":[{"given":"Endre","family":"Boros","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ond\u0159ej","family":"\u010cepek","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kazuhisa","family":"Makino","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,8,16]]},"reference":[{"key":"11_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-04414-4_16","volume-title":"Algorithmic Learning Theory","author":"M Arias","year":"2009","unstructured":"Arias, M., Balc\u00e1zar, J.L.: Canonical Horn representations and query learning. In: Gavald\u00e0, R., Lugosi, G., Zeugmann, T., Zilles, S. (eds.) ALT 2009. LNCS, vol. 5809. Springer, Heidelberg (2009). doi:\n10.1007\/978-3-642-04414-4_16"},{"issue":"3","key":"11_CR2","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1007\/s10994-011-5248-5","volume":"85","author":"M Arias","year":"2011","unstructured":"Arias, M., Balc\u00e1zar, J.L.: Construction and learnability of canonical Horn formulas. Mach. Learn. 85(3), 273\u2013297 (2011)","journal-title":"Mach. Learn."},{"issue":"2","key":"11_CR3","doi-asserted-by":"crossref","first-page":"418","DOI":"10.1137\/0215029","volume":"15","author":"G Ausiello","year":"1986","unstructured":"Ausiello, G., D\u2019Atri, A., Sacca, D.: Minimal representation of directed hypergraphs. SIAM J. Comput. 15(2), 418\u2013431 (1986)","journal-title":"SIAM J. Comput."},{"issue":"3\u20134","key":"11_CR4","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1023\/A:1018932728409","volume":"23","author":"E Boros","year":"1998","unstructured":"Boros, E., \u010cepek, O., Kogan, A.: Horn minimization by iterative decomposition. Ann. Math. Artif. Intell. 23(3\u20134), 321\u2013343 (1998)","journal-title":"Ann. Math. Artif. Intell."},{"issue":"3\u20134","key":"11_CR5","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1007\/s10472-010-9197-7","volume":"57","author":"E Boros","year":"2009","unstructured":"Boros, E., \u010cepek, O., Kogan, A., Ku\u010dera, P.: A subclass of Horn CNFs optimally compressible in polynomial time. Ann. Math. Artif. Intell. 57(3\u20134), 249\u2013291 (2009)","journal-title":"Ann. Math. Artif. Intell."},{"issue":"2","key":"11_CR6","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/j.dam.2009.08.012","volume":"158","author":"E Boros","year":"2010","unstructured":"Boros, E., \u010cepek, O., Kogan, A., Ku\u010dera, P.: Exclusive and essential sets of implicates of Boolean functions. Discret. Appl. Math. 158(2), 81\u201396 (2010)","journal-title":"Discret. Appl. Math."},{"key":"11_CR7","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/j.tcs.2013.09.016","volume":"510","author":"E Boros","year":"2013","unstructured":"Boros, E., \u010cepek, O., Ku\u010dera, P.: A decomposition method for CNF minimality proofs. Theoret. Comput. Sci. 510, 111\u2013126 (2013)","journal-title":"Theoret. Comput. Sci."},{"issue":"1","key":"11_CR8","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1016\/j.jcss.2010.06.011","volume":"77","author":"D Buchfuhrer","year":"2011","unstructured":"Buchfuhrer, D., Umans, C.: The complexity of Boolean formula minimization. J. Comput. Syst. Sci. 77(1), 142\u2013153 (2011). Celebrating Karp\u2019s Kyoto Prize","journal-title":"J. Comput. Syst. Sci."},{"key":"11_CR9","doi-asserted-by":"crossref","unstructured":"Cook, S.A.: The complexity of theorem-proving procedures. In: Proceedings of the Third Annual ACM Symposium on Theory of Computing, STOC 1971, pp. 151\u2013158. ACM, New York (1971)","DOI":"10.1145\/800157.805047"},{"issue":"4\u20135","key":"11_CR10","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1016\/j.dam.2011.05.013","volume":"160","author":"O \u010cepek","year":"2012","unstructured":"\u010cepek, O., Ku\u010dera, P., Savicky, P.: Boolean functions with a simple certificate for CNF complexity. Discret. Appl. Math. 160(4\u20135), 365\u2013382 (2012)","journal-title":"Discret. Appl. Math."},{"key":"11_CR11","first-page":"5","volume":"95","author":"JL Guigues","year":"1986","unstructured":"Guigues, J.L., Duquenne, V.: Familles minimales d\u2019implications informatives r\u00e9sultant d\u2019une tables de donn\u00e9es binares. Math. Sci. Hum. 95, 5\u201318 (1986)","journal-title":"Math. Sci. Hum."},{"issue":"1","key":"11_CR12","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/0004-3702(93)90062-G","volume":"64","author":"PL Hammer","year":"1993","unstructured":"Hammer, P.L., Kogan, A.: Optimal compression of propositional Horn knowledge bases: complexity and approximation. Artif. Intell. 64(1), 131\u2013145 (1993)","journal-title":"Artif. Intell."},{"issue":"5","key":"11_CR13","doi-asserted-by":"crossref","first-page":"751","DOI":"10.1109\/69.469822","volume":"7","author":"PL Hammer","year":"1995","unstructured":"Hammer, P.L., Kogan, A.: Quasi-acyclic propositional Horn knowledge bases: optimal compression. IEEE Trans. Knowl. Data Eng. 7(5), 751\u2013762 (1995)","journal-title":"IEEE Trans. Knowl. Data Eng."},{"issue":"1","key":"11_CR14","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/j.dam.2012.07.004","volume":"161","author":"L Hellerstein","year":"2013","unstructured":"Hellerstein, L., Kletenik, D.: On the gap between ess\n            $$(f)$$\n           and cnf-size\n            $$(f)$$\n          . Discret. Appl. Math. 161(1), 19\u201327 (2013)","journal-title":"Discret. Appl. Math."},{"issue":"4","key":"11_CR15","doi-asserted-by":"crossref","first-page":"664","DOI":"10.1145\/322217.322223","volume":"27","author":"D Maier","year":"1980","unstructured":"Maier, D.: Minimum covers in relational database model. J. ACM 27(4), 664\u2013674 (1980)","journal-title":"J. ACM"},{"issue":"4","key":"11_CR16","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1006\/jcss.2001.1775","volume":"63","author":"C Umans","year":"2001","unstructured":"Umans, C.: The minimum equivalent DNF problem and shortest implicants. J. Comput. Syst. Sci. 63(4), 597\u2013611 (2001)","journal-title":"J. Comput. Syst. Sci."},{"issue":"7","key":"11_CR17","doi-asserted-by":"crossref","first-page":"1230","DOI":"10.1109\/TCAD.2005.855944","volume":"25","author":"C Umans","year":"2006","unstructured":"Umans, C., Villa, T., Sangiovanni-Vincentelli, A.L.: Complexity of two-level logic minimization. IEEE Trans. Comput.-Aided Des. Integr. Circ. Syst. 25(7), 1230\u20131246 (2006)","journal-title":"IEEE Trans. Comput.-Aided Des. Integr. Circ. Syst."}],"container-title":["Lecture Notes in Computer Science","Fundamentals of Computation Theory"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-662-55751-8_11","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,8,15]],"date-time":"2017-08-15T11:35:28Z","timestamp":1502796928000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-662-55751-8_11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017]]},"ISBN":["9783662557501","9783662557518"],"references-count":17,"URL":"https:\/\/doi.org\/10.1007\/978-3-662-55751-8_11","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2017]]}}}