{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,7,29]],"date-time":"2023-07-29T07:29:34Z","timestamp":1690615774409},"reference-count":52,"publisher":"Elsevier BV","issue":"1-3","license":[{"start":{"date-parts":[[2003,2,1]],"date-time":"2003-02-01T00:00:00Z","timestamp":1044057600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2013,7,17]],"date-time":"2013-07-17T00:00:00Z","timestamp":1374019200000},"content-version":"vor","delay-in-days":3819,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Theoretical Computer Science"],"published-print":{"date-parts":[[2003,2]]},"DOI":"10.1016\/s0304-3975(02)00412-7","type":"journal-article","created":{"date-parts":[[2003,2,28]],"date-time":"2003-02-28T19:20:13Z","timestamp":1046460013000},"page":"341-370","source":"Crossref","is-referenced-by-count":8,"title":["On the equational definition of the least prefixed point"],"prefix":"10.1016","volume":"295","author":[{"given":"Luigi","family":"Santocanale","sequence":"first","affiliation":[]}],"member":"78","reference":[{"issue":"1","key":"10.1016\/S0304-3975(02)00412-7_BIB1","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/0304-3975(95)00045-X","article-title":"Duality and the completeness of the modal \u03bc-calculus","volume":"151","author":"Ambler","year":"1995","journal-title":"Theoret. Comput. Sci."},{"issue":"4\u20135","key":"10.1016\/S0304-3975(02)00412-7_BIB2","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1051\/ita:1999121","article-title":"The \u03bc-calculus alternation-depth hierarchy is strict on binary trees","volume":"33","author":"Arnold","year":"1999","journal-title":"Theory Inform. Appl."},{"key":"10.1016\/S0304-3975(02)00412-7_BIB3","article-title":"Rudiments of mu-calculus","volume":"Vol. 2146","author":"Arnold","year":"2001"},{"key":"10.1016\/S0304-3975(02)00412-7_BIB4","first-page":"A1501","article-title":"Cat\u00e9gories exactes","volume":"272","author":"Barr","year":"1971","journal-title":"C.R. Acad. Sci. Paris S\u00e9r. A-B"},{"issue":"2","key":"10.1016\/S0304-3975(02)00412-7_BIB5","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1093\/logcom\/12.2.243","article-title":"Monadic logic of order over naturals has no finite base","volume":"12","author":"Beauquier","year":"2002","journal-title":"J. Logic Comput."},{"issue":"2","key":"10.1016\/S0304-3975(02)00412-7_BIB6","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1016\/S0022-0000(76)80030-X","article-title":"Varieties of ordered algebras","volume":"13","author":"Bloom","year":"1976","journal-title":"J. Comput. System Sci."},{"key":"10.1016\/S0304-3975(02)00412-7_BIB7","series-title":"Iteration Theories","author":"Bloom","year":"1993"},{"issue":"1","key":"10.1016\/S0304-3975(02)00412-7_BIB8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1017\/S0960129500000104","article-title":"Equational axioms for regular sets","volume":"3","author":"Bloom","year":"1993","journal-title":"Math. Struct. Comput. Sci."},{"key":"10.1016\/S0304-3975(02)00412-7_BIB9","first-page":"150","article-title":"Two axiomatizations of a star semiring quasi-variety","volume":"59","author":"Bloom","year":"1996","journal-title":"Bull. European Assoc. Theoret. Comp. Sci."},{"issue":"4","key":"10.1016\/S0304-3975(02)00412-7_BIB10","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1051\/ita\/1990240404191","article-title":"Une remarque sur les syst\u00e8mes complets d'identit\u00e9s rationnelles","volume":"24","author":"Boffa","year":"1990","journal-title":"RAIRO Inform. Th\u00e9or. Appl."},{"issue":"6","key":"10.1016\/S0304-3975(02)00412-7_BIB11","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1051\/ita\/1995290605151","article-title":"Une condition impliquant toutes les identit\u00e9s rationnelles","volume":"29","author":"Boffa","year":"1995","journal-title":"RAIRO Inform. Th\u00e9or. Appl."},{"issue":"2","key":"10.1016\/S0304-3975(02)00412-7_BIB12","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/S0304-3975(97)00217-X","article-title":"The modal mu-calculus alternation hierarchy is strict","volume":"195","author":"Bradfield","year":"1998","journal-title":"Theoret. Comput. Sci."},{"issue":"3","key":"10.1016\/S0304-3975(02)00412-7_BIB13","first-page":"249","article-title":"Alg\u00e8bres graphiques: sur un concept de dimension dans les langages formels","volume":"22","author":"Burroni","year":"1981","journal-title":"Cahiers Topologie G\u00e9om. Diff\u00e9rentielle"},{"key":"10.1016\/S0304-3975(02)00412-7_BIB14","series-title":"Regular Algebra and Finite Machines","author":"Conway","year":"1971"},{"issue":"1","key":"10.1016\/S0304-3975(02)00412-7_BIB15","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1016\/S0304-3975(96)00240-X","article-title":"Completeness of Park induction","volume":"177","author":"\u00c9sik","year":"1997","journal-title":"Theoret. Comput. Sci."},{"issue":"2","key":"10.1016\/S0304-3975(02)00412-7_BIB16","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1006\/inco.1998.2746","article-title":"Group axioms for iteration","volume":"148","author":"\u00c9sik","year":"1999","journal-title":"Inform. Comput."},{"issue":"1","key":"10.1016\/S0304-3975(02)00412-7_BIB17","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/S0304-3975(97)00158-8","article-title":"Equational properties of iteration in algebraically complete categories","volume":"195","author":"\u00c9sik","year":"1998","journal-title":"Theoret. Comput. Sci."},{"key":"10.1016\/S0304-3975(02)00412-7_BIB18","series-title":"Category Theory (Como, 1990)","first-page":"95","article-title":"Algebraically complete categories","author":"Freyd","year":"1991"},{"key":"10.1016\/S0304-3975(02)00412-7_BIB19","series-title":"Categories, Allegories","author":"Freyd","year":"1990"},{"key":"10.1016\/S0304-3975(02)00412-7_BIB20","doi-asserted-by":"crossref","unstructured":"D.M. Gabbay, I. Hodkinson, M. Reynolds, Temporal Logic, Vol. 1, The Clarendon Press, Oxford University Press, New York, 1994.","DOI":"10.1007\/BFb0013976"},{"key":"10.1016\/S0304-3975(02)00412-7_BIB21","series-title":"Universal Algebra","author":"Gr\u00e4tzer","year":"1979"},{"issue":"1\u20132","key":"10.1016\/S0304-3975(02)00412-7_BIB22","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/S0304-3975(97)00233-8","article-title":"Duality for modal \u03bc-logics","volume":"202","author":"Hartonas","year":"1998","journal-title":"Theoret. Comput. Sci."},{"key":"10.1016\/S0304-3975(02)00412-7_BIB23","series-title":"Dynamic Logic","author":"Harel","year":"2000"},{"key":"10.1016\/S0304-3975(02)00412-7_BIB24","doi-asserted-by":"crossref","unstructured":"S.C. Kleene, Representation of events in nerve nets and finite automata, in: Automata studies, Princeton University Press, Princeton, NJ., 1956, pp. 3\u201341.","DOI":"10.1515\/9781400882618-002"},{"issue":"3","key":"10.1016\/S0304-3975(02)00412-7_BIB25","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1016\/0304-3975(82)90125-6","article-title":"Results on the propositional \u03bc-calculus","volume":"27","author":"Kozen","year":"1983","journal-title":"Theoret. Comput. Sci."},{"key":"10.1016\/S0304-3975(02)00412-7_BIB26","series-title":"Mathematical Foundations of Computer Science (Bansk\u00e1 Bystrica, 1990)","first-page":"26","article-title":"On Kleene algebras and closed semirings","volume":"Vol. 452","author":"Kozen","year":"1990"},{"issue":"2","key":"10.1016\/S0304-3975(02)00412-7_BIB27","doi-asserted-by":"crossref","first-page":"366","DOI":"10.1006\/inco.1994.1037","article-title":"A completeness theorem for Kleene algebras and the algebra of regular events","volume":"110","author":"Kozen","year":"1994","journal-title":"Inform. Comput."},{"issue":"2","key":"10.1016\/S0304-3975(02)00412-7_BIB28","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/0304-3975(91)90395-I","article-title":"Complete systems of B-rational identities","volume":"89","author":"Krob","year":"1991","journal-title":"Theoret. Comput. Sci."},{"key":"10.1016\/S0304-3975(02)00412-7_BIB29","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1007\/BF01110627","article-title":"A fixpoint theorem for complete categories","volume":"103","author":"Lambek","year":"1968","journal-title":"Math. Z."},{"issue":"1\u20133","key":"10.1016\/S0304-3975(02)00412-7_BIB30","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1016\/S0022-4049(99)00178-4","article-title":"An equational variant of Lawvere's natural numbers object","volume":"154","author":"Lambek","year":"2000","journal-title":"J. Pure Appl. Algebra"},{"key":"10.1016\/S0304-3975(02)00412-7_BIB31","series-title":"Introduction to Higher Order Categorical Logic","author":"Lambek","year":"1988"},{"key":"10.1016\/S0304-3975(02)00412-7_BIB32","series-title":"Automata, Languages and Programming","first-page":"87","article-title":"A hierarchy theorem for the \u03bc-calculus","volume":"Vol. 1099","author":"Lenzi","year":"1996"},{"key":"10.1016\/S0304-3975(02)00412-7_BIB33","series-title":"Categories for the Working Mathematician","author":"Mac Lane","year":"1998"},{"key":"10.1016\/S0304-3975(02)00412-7_BIB34","unstructured":"L. Moss, Recursion and corecursion have the same equational logic, preprint, May 2001."},{"issue":"1","key":"10.1016\/S0304-3975(02)00412-7_BIB35","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/0304-3975(83)90014-2","article-title":"Iterative algebras","volume":"25","author":"Nelson","year":"1983","journal-title":"Theoret. Comput. Sci."},{"key":"10.1016\/S0304-3975(02)00412-7_BIB36","unstructured":"K. Ng, Relation algebras with transitive closure, Ph.D. Thesis, University of California, Berkeley, 1984."},{"key":"10.1016\/S0304-3975(02)00412-7_BIB37","unstructured":"K. Ng, A. Tarski, Relational algebras with transitive closure, Notices Amer. Math. Soc. 24 A29\u2013A30 (abstract 742-02-09) (1977)."},{"key":"10.1016\/S0304-3975(02)00412-7_BIB38","series-title":"Computation Theory (Zabor\u00f3w, 1984)","first-page":"169","article-title":"Equational \u03bc-calculus","volume":"Vol. 208","author":"Niwi\u0144ski","year":"1995"},{"key":"10.1016\/S0304-3975(02)00412-7_BIB39","series-title":"Automata, Languages and Programming (Rennes, 1986)","first-page":"464","article-title":"On fixed-point clones (extended abstract)","volume":"Vol. 226","author":"Niwi\u0144ski","year":"1986"},{"key":"10.1016\/S0304-3975(02)00412-7_BIB40","unstructured":"D. Park, Fixpoint induction and proofs of program properties, in: Machine Intelligence, Vol. 5, American Elsevier, New York, 1970, pp. 59\u201378."},{"key":"10.1016\/S0304-3975(02)00412-7_BIB41","doi-asserted-by":"crossref","unstructured":"V. Pratt, Action logic and pure induction, in: J. van Eijck (Ed.), Logics in AI (Amsterdam, 1990), Springer, Berlin, 1991, pp. 97\u2013120.","DOI":"10.1007\/BFb0018436"},{"issue":"3-4","key":"10.1016\/S0304-3975(02)00412-7_BIB42","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1007\/BF00370685","article-title":"Dynamic algebras","volume":"50","author":"Pratt","year":"1991","journal-title":"Stud. Logica"},{"key":"10.1016\/S0304-3975(02)00412-7_BIB43","first-page":"120","article-title":"On the determining totality of relations of an algebra of regular events","volume":"16","author":"Red'ko","year":"1964","journal-title":"Ukrain. Mat. \u017d."},{"key":"10.1016\/S0304-3975(02)00412-7_BIB44","series-title":"Quantales and their Applications","author":"Rosenthal","year":"1990"},{"key":"10.1016\/S0304-3975(02)00412-7_BIB45","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1145\/321312.321326","article-title":"Two complete axiom systems for the algebra of regular events","volume":"13","author":"Salomaa","year":"1966","journal-title":"J. Assoc. Comput. Mach."},{"key":"10.1016\/S0304-3975(02)00412-7_BIB46","unstructured":"L. Santocanale, Sur les \u03bc-treillis libres, Ph.D. Thesis, Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al, July 2000."},{"issue":"2\u20133","key":"10.1016\/S0304-3975(02)00412-7_BIB47","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1016\/S0022-4049(01)00098-6","article-title":"Free \u03bc-lattices","volume":"168","author":"Santocanale","year":"2002","journal-title":"J. Pure Appl. Algebra"},{"key":"10.1016\/S0304-3975(02)00412-7_BIB48","first-page":"166","article-title":"The alternation hierarchy for the theory of \u03bc-lattices","volume":"9","author":"Santocanale","year":"2002","journal-title":"Theory Appl. Categ."},{"key":"10.1016\/S0304-3975(02)00412-7_BIB49","unstructured":"K. Segerberg, A completeness theorem in the modal logic of programs, Notices Amer. Math. Soc 24 A552 (abstract 77T-E69) (1977)."},{"key":"10.1016\/S0304-3975(02)00412-7_BIB50","doi-asserted-by":"crossref","unstructured":"A.K. Simpson, G.D. Plotkin, Complete axioms for categorical fixed-point operators, in: Proc. 15th Annu. IEEE Symp. on Logic in Computer Science, IEEE, New York, 2000.","DOI":"10.1109\/LICS.2000.855753"},{"issue":"1\u20132","key":"10.1016\/S0304-3975(02)00412-7_BIB51","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1006\/inco.1999.2836","article-title":"Completeness of Kozen's axiomatisation of the propositional \u03bc-calculus","volume":"157","author":"Walukiewicz","year":"2000","journal-title":"Inform. Comput."},{"issue":"2","key":"10.1016\/S0304-3975(02)00412-7_BIB52","doi-asserted-by":"crossref","first-page":"104","DOI":"10.2307\/1968883","article-title":"Free lattices","volume":"43","author":"Whitman","year":"1942","journal-title":"II, Ann. Math."}],"container-title":["Theoretical Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0304397502004127?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0304397502004127?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2020,3,12]],"date-time":"2020-03-12T07:23:03Z","timestamp":1583997783000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0304397502004127"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,2]]},"references-count":52,"journal-issue":{"issue":"1-3","published-print":{"date-parts":[[2003,2]]}},"alternative-id":["S0304397502004127"],"URL":"https:\/\/doi.org\/10.1016\/s0304-3975(02)00412-7","relation":{},"ISSN":["0304-3975"],"issn-type":[{"value":"0304-3975","type":"print"}],"subject":[],"published":{"date-parts":[[2003,2]]}}}