{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,20]],"date-time":"2025-02-20T23:59:54Z","timestamp":1740095994856,"version":"3.37.3"},"publisher-location":"Berlin, Heidelberg","reference-count":18,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642151545"},{"type":"electronic","value":"9783642151552"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2010]]},"DOI":"10.1007\/978-3-642-15155-2_39","type":"book-chapter","created":{"date-parts":[[2010,8,13]],"date-time":"2010-08-13T20:17:45Z","timestamp":1281730665000},"page":"441-452","source":"Crossref","is-referenced-by-count":3,"title":["Least and Greatest Solutions of Equations over Sets of Integers"],"prefix":"10.1007","author":[{"given":"Artur","family":"Je\u017c","sequence":"first","affiliation":[]},{"given":"Alexander","family":"Okhotin","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"39_CR1","doi-asserted-by":"publisher","first-page":"350","DOI":"10.1145\/321127.321132","volume":"9","author":"S. Ginsburg","year":"1962","unstructured":"Ginsburg, S., Rice, H.G.: Two families of languages related to ALGOL. Journal of the ACM\u00a09, 350\u2013371 (1962)","journal-title":"Journal of the ACM"},{"issue":"3","key":"39_CR2","doi-asserted-by":"publisher","first-page":"597","DOI":"10.1142\/S012905410800584X","volume":"19","author":"A. Je\u017c","year":"2008","unstructured":"Je\u017c, A.: Conjunctive grammars can generate non-regular unary languages. International Journal of Foundations of Computer Science\u00a019(3), 597\u2013615 (2008)","journal-title":"International Journal of Foundations of Computer Science"},{"issue":"1","key":"39_CR3","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1007\/s00224-008-9139-5","volume":"46","author":"A. Je\u017c","year":"2010","unstructured":"Je\u017c, A., Okhotin, A.: Conjunctive grammars over a unary alphabet: undecidability and unbounded growth. Theory of Computing Systems\u00a046(1), 27\u201358 (2010), \n                  \n                    http:\/\/dx.doi.org\/10.1007\/s00224-008-9139-5","journal-title":"Theory of Computing Systems"},{"key":"39_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1007\/978-3-540-70583-3_6","volume-title":"Automata, Languages and Programming","author":"A. Je\u017c","year":"2008","unstructured":"Je\u017c, A., Okhotin, A.: On the computational completeness of equations over sets of natural numbers. In: Aceto, L., Damg\u00e5rd, I., Goldberg, L.A., Halld\u00f3rsson, M.M., Ing\u00f3lfsd\u00f3ttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part II. LNCS, vol.\u00a05126, pp. 63\u201374. Springer, Heidelberg (2008)"},{"key":"39_CR5","unstructured":"Je\u017c, A., Okhotin, A.: Equations over sets of natural numbers with addition only. In: STACS 2009, Freiburg, Germany, February 26-28, pp. 577\u2013588 (2009)"},{"key":"39_CR6","unstructured":"Je\u017c, A., Okhotin, A.: On equations over sets of integers. In: STACS 2010, Nancy, France, March 4-6, pp. 477\u2013488 (2010)"},{"key":"39_CR7","volume-title":"Introduction to metamathematics","author":"S.C. Kleene","year":"1952","unstructured":"Kleene, S.C.: Introduction to metamathematics. North-Holland, Amsterdam (1952)"},{"key":"39_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1007\/978-3-540-73208-2_3","volume-title":"Developments in Language Theory","author":"M. Kunc","year":"2007","unstructured":"Kunc, M.: What do we know about language equations? In: Harju, T., Karhum\u00e4ki, J., Lepist\u00f6, A. (eds.) DLT 2007. LNCS, vol.\u00a04588, pp. 23\u201327. Springer, Heidelberg (2007)"},{"key":"39_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1007\/978-3-642-14455-4_27","volume-title":"DLT 2010","author":"T. Lehtinen","year":"2010","unstructured":"Lehtinen, T., Okhotin, A.: On language equations XXK\u2009=\u2009XXL and XM\u2009=\u2009N over a unary alphabet. In: Yu, S. (ed.) DLT 2010. LNCS, vol.\u00a06224, pp. 291\u2013302. Springer, Heidelberg (2010)"},{"issue":"3","key":"39_CR10","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1007\/s00037-007-0229-6","volume":"16","author":"P. McKenzie","year":"2007","unstructured":"McKenzie, P., Wagner, K.: The complexity of membership problems for circuits over sets of natural numbers. Computational Complexity\u00a016(3), 211\u2013244 (2007)","journal-title":"Computational Complexity"},{"issue":"4","key":"39_CR11","first-page":"519","volume":"6","author":"A. Okhotin","year":"2001","unstructured":"Okhotin, A.: Conjunctive grammars. Journal of Automata, Languages and Combinatorics\u00a06(4), 519\u2013535 (2001)","journal-title":"Journal of Automata, Languages and Combinatorics"},{"issue":"5","key":"39_CR12","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1023\/A:1020213411126","volume":"28","author":"A. Okhotin","year":"2002","unstructured":"Okhotin, A.: Conjunctive grammars and systems of language equations. Programming and Computer Software\u00a028(5), 243\u2013249 (2002)","journal-title":"Programming and Computer Software"},{"issue":"1","key":"39_CR13","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1051\/ita:2004004","volume":"38","author":"A. Okhotin","year":"2004","unstructured":"Okhotin, A.: On the equivalence of linear conjunctive grammars to trellis automata. Informatique Th\u00e9orique et Applications\u00a038(1), 69\u201388 (2004)","journal-title":"Informatique Th\u00e9orique et Applications"},{"key":"39_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"708","DOI":"10.1007\/11549345_61","volume-title":"Mathematical Foundations of Computer Science 2005","author":"A. Okhotin","year":"2005","unstructured":"Okhotin, A.: Strict language inequalities and their decision problems. In: Jedrzejowicz, J., Szepietowski, A. (eds.) MFCS 2005. LNCS, vol.\u00a03618, pp. 708\u2013719. Springer, Heidelberg (2005)"},{"issue":"3-4","key":"39_CR15","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1016\/j.jcss.2009.08.002","volume":"76","author":"A. Okhotin","year":"2010","unstructured":"Okhotin, A.: Decision problems for language equations. Journal of Computer and System Sciences\u00a076(3-4), 251\u2013266 (2010)","journal-title":"Journal of Computer and System Sciences"},{"key":"39_CR16","volume-title":"Theory of Recursive Functions and Effective Computability","author":"H. Rogers Jr.","year":"1967","unstructured":"Rogers Jr., H.: Theory of Recursive Functions and Effective Computability. McGraw-Hill, New York (1967)"},{"key":"39_CR17","doi-asserted-by":"crossref","first-page":"285","DOI":"10.2140\/pjm.1955.5.285","volume":"5","author":"A. Tarski","year":"1955","unstructured":"Tarski, A.: A lattice theoretical fixpoint theorem and its applications. Pacific Journal of Mathematics\u00a05, 285\u2013310 (1955)","journal-title":"Pacific Journal of Mathematics"},{"issue":"1-3","key":"39_CR18","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1016\/j.tcs.2006.08.017","volume":"369","author":"S.D. Travers","year":"2006","unstructured":"Travers, S.D.: The complexity of membership problems for circuits over sets of integers. Theoretical Computer Science\u00a0369(1-3), 211\u2013229 (2006)","journal-title":"Theoretical Computer Science"}],"container-title":["Lecture Notes in Computer Science","Mathematical Foundations of Computer Science 2010"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-15155-2_39.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,24]],"date-time":"2020-11-24T03:01:43Z","timestamp":1606186903000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-15155-2_39"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010]]},"ISBN":["9783642151545","9783642151552"],"references-count":18,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-15155-2_39","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2010]]}}}