{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,4]],"date-time":"2025-12-04T09:48:26Z","timestamp":1764841706448},"publisher-location":"Berlin, Heidelberg","reference-count":14,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642325885"},{"type":"electronic","value":"9783642325892"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2012]]},"DOI":"10.1007\/978-3-642-32589-2_54","type":"book-chapter","created":{"date-parts":[[2012,8,1]],"date-time":"2012-08-01T08:44:32Z","timestamp":1343810672000},"page":"615-629","source":"Crossref","is-referenced-by-count":2,"title":["Equations X\u2009+\u2009A\u2009=\u2009B and (X\u2009+\u2009X)\u2009+\u2009C\u2009=\u2009(X\u2009\u2212\u2009X)\u2009+\u2009D over Sets of Natural Numbers"],"prefix":"10.1007","author":[{"given":"Tommi","family":"Lehtinen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"54_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":"54_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"},{"key":"54_CR3","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":"54_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1007\/978-3-642-15155-2_39","volume-title":"Mathematical Foundations of Computer Science 2010","author":"A. Je\u017c","year":"2010","unstructured":"Je\u017c, A., Okhotin, A.: Least and Greatest Solutions of Equations over Sets of Integers. In: Hlin\u011bn\u00fd, P., Ku\u010dera, A. (eds.) MFCS 2010. LNCS, vol.\u00a06281, pp. 441\u2013452. Springer, Heidelberg (2010)"},{"key":"54_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1007\/978-3-540-70583-3_6","volume-title":"Automata, Languages and Programming, Part II","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":"54_CR6","unstructured":"Je\u017c, A., Okhotin, A.: Representing hyper-arithmetical sets by equations over sets of integers. Theory of Computing Systems (accepted)"},{"issue":"4","key":"54_CR7","doi-asserted-by":"publisher","first-page":"521","DOI":"10.1007\/s00224-006-1321-z","volume":"40","author":"M. Kunc","year":"2007","unstructured":"Kunc, M.: The power of commuting with finite sets of words. Theory of Computing Systems\u00a040(4), 521\u2013551 (2007)","journal-title":"Theory of Computing Systems"},{"key":"54_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)"},{"issue":"2","key":"54_CR9","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1142\/S012905411100809X","volume":"22","author":"T. Lehtinen","year":"2011","unstructured":"Lehtinen, T., Okhotin, A.: On equations over sets of numbers and their limitations. International Journal of Foundations of Computer Science\u00a022(2), 377\u2013393 (2011)","journal-title":"International Journal of Foundations of Computer Science"},{"key":"54_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1007\/978-3-642-14455-4_27","volume-title":"Developments in Language Theory","author":"T. Lehtinen","year":"2010","unstructured":"Lehtinen, T., Okhotin, A.: On Language Equations XXK = XXL and XM = N over a Unary Alphabet. In: Gao, Y., Lu, H., Seki, S., Yu, S. (eds.) DLT 2010. LNCS, vol.\u00a06224, pp. 291\u2013302. Springer, Heidelberg (2010)"},{"key":"54_CR11","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1016\/0304-3975(94)90227-5","volume":"132","author":"E.L. Leiss","year":"1994","unstructured":"Leiss, E.L.: Unrestricted complementation in language equations over a one-letter alphabet. Theoretical Computer Science\u00a0132, 71\u201393 (1994)","journal-title":"Theoretical Computer Science"},{"issue":"4","key":"54_CR12","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":"3-4","key":"54_CR13","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"},{"issue":"3","key":"54_CR14","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1016\/j.tcs.2005.07.038","volume":"349","author":"A. Okhotin","year":"2005","unstructured":"Okhotin, A.: Unresolved systems of language equations: expressive power and decision problems. Theoretical Computer Science\u00a0349(3), 283\u2013308 (2005)","journal-title":"Theoretical Computer Science"}],"container-title":["Lecture Notes in Computer Science","Mathematical Foundations of Computer Science 2012"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-32589-2_54.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,5,4]],"date-time":"2021-05-04T12:08:14Z","timestamp":1620130094000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-32589-2_54"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012]]},"ISBN":["9783642325885","9783642325892"],"references-count":14,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-32589-2_54","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2012]]}}}