{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T00:42:37Z","timestamp":1725496957692},"publisher-location":"Berlin, Heidelberg","reference-count":21,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540418641"},{"type":"electronic","value":"9783540453154"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2001]]},"DOI":"10.1007\/3-540-45315-6_3","type":"book-chapter","created":{"date-parts":[[2007,12,3]],"date-time":"2007-12-03T06:28:39Z","timestamp":1196663319000},"page":"42-56","source":"Crossref","is-referenced-by-count":0,"title":["Axiomatizing Tropical Semirings"],"prefix":"10.1007","author":[{"given":"Luca","family":"Aceto","sequence":"first","affiliation":[]},{"given":"Zolt\u00e1n","family":"\u00c9sik","sequence":"additional","affiliation":[]},{"given":"Anna","family":"Ing\u00f3lfsd\u00f3ttir","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2001,3,23]]},"reference":[{"key":"3_CR1","doi-asserted-by":"crossref","unstructured":"L. Aceto, Z. \u00c9sik, and A. Ing\u00d3lfsd\u00d3ttir, The max-plus algebra of the natural numbers has no finite equational basis, BRICS Report RS-99-33, October 1999. To appear in Theoretical Computer Science.","DOI":"10.7146\/brics.v6i33.20102"},{"key":"3_CR2","series-title":"Lect Notes Comput Sci","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1007\/3-540-46541-3_22","volume-title":"Proceedings of the 17th STACS","author":"L. Aceto","year":"2000","unstructured":"\u2014 On the two-variable fragment of the equational theory of the max-sum algebra of the natural numbers, in Proceedings of the 17th STACS, H. Reichel and S. Tison, eds., vol. 1770 of Lecture Notes in Computer Science, Springer-Verlag, Feb. 2000, pp. 267\u2013278."},{"key":"3_CR3","unstructured":"\u2014 Nonfinitely based tropical semirings, in Proceedings of the Int. Workshop on Max-Plus Algebras, Praha, August, 2001, to appear. 4., Axiomatizing tropical semirings, to appear as BRICS research report."},{"key":"3_CR4","unstructured":"F. Baccelli, G. Cohen, G.-J. Olsder, and J.-P. Quadrat, Synchronization and Linearity, Wiley Series in Probability and Mathematical Statistics, John Wiley, 1992."},{"key":"3_CR5","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1016\/0304-3975(94)90276-3","volume":"134","author":"A. Bonnier-Rigny","year":"1994","unstructured":"A. Bonnier-Rigny and D. Krob, A complete system of identities for one-letter rational expressions with multiplicities in the tropical semiring, Theoretical Computer Science, 134 (1994), pp. 27\u201350.","journal-title":"Theoretical Computer Science"},{"key":"3_CR6","unstructured":"W. Burnside, On an unsettled question in the theory of discontinuous groups, Q. J. Pure and Appl. Mathematics, 33 (1902), pp. 230\u2013238."},{"key":"3_CR7","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4613-8130-3","volume-title":"A Course in Universal Algebra","author":"S. Burris","year":"1981","unstructured":"S. Burris and H. P. Sankappanavar, A Course in Universal Algebra, Springer-Verlag, New York, 1981."},{"key":"3_CR8","volume-title":"Mathematics Series","author":"J. H. Conway","year":"1971","unstructured":"J. H. Conway, Regular Algebra and Finite Machines, Mathematics Series (R. Brown and J. De Wet eds.), Chapman and Hall, London, United Kingdom, 1971."},{"key":"3_CR9","doi-asserted-by":"crossref","unstructured":"J. Gunawardena (ed.), Idempotency, Publications of the Newton Institute 11, Cambridge University Press, 1998.","DOI":"10.1017\/CBO9780511662508"},{"key":"3_CR10","unstructured":"\u2014 An introduction to idempotency, in [10], pp. 1\u201349."},{"issue":"2","key":"3_CR11","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1016\/0022-0000(82)90051-4","volume":"24","author":"K. Hashiguchi","year":"1982","unstructured":"K. Hashiguchi, Limitedness theorem on finite automata with distance functions, J. Comput. System Sci., 24 (1982), no. 2, pp. 233\u2013244.","journal-title":"J. Comput. System Sci."},{"key":"3_CR12","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1016\/S0019-9958(82)91028-2","volume":"53","author":"K. Hashiguchi","year":"1982","unstructured":"\u2014 Regular languages of star height one, Information and Control, 53 (1982), pp. 199\u2013210.","journal-title":"Information and Control"},{"key":"3_CR13","doi-asserted-by":"publisher","first-page":"124","DOI":"10.1016\/0890-5401(88)90033-8","volume":"78","author":"K. Hashiguchi","year":"1988","unstructured":"\u2014 Algorithms for determining relative star height and star height, Information and Computation, 78 (1988), pp. 124\u2013169.","journal-title":"Information and Computation"},{"key":"3_CR14","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1142\/S0218196794000063","volume":"4","author":"D. Krob","year":"1994","unstructured":"D. Krob, The equality problem for rational series with multiplicities in the tropical semiring is undecidable, International J. Algebra Computation, 4 (1994), pp. 405\u2013425.","journal-title":"International J. Algebra Computation"},{"key":"3_CR15","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1016\/0022-4049(94)90090-6","volume":"93","author":"D. Krob","year":"1994","unstructured":"\u2014 Some consequences of a Fatou property of the tropical semiring, Journal of Pure and Applied Algebra, 93 (1994), pp. 231\u2013249.","journal-title":"Journal of Pure and Applied Algebra"},{"key":"3_CR16","unstructured":"\u2014 Some automata-theoretic aspects of min-max-plus semirings, in [10], pp. 70\u201379."},{"key":"3_CR17","doi-asserted-by":"crossref","unstructured":"J.-E. Pin, Tropical semirings, in [10], pp. 50\u201369.","DOI":"10.1017\/CBO9780511662508.004"},{"key":"3_CR18","unstructured":"A. Schrijver, Theory of Linear and Integer Programming, John Wiley and Sons, 1986."},{"key":"3_CR19","doi-asserted-by":"crossref","unstructured":"I. Simon, Limited subsets of a free monoid, in Proceedings of the 19th Annual Symposium on Foundations of Computer Science (Ann Arbor, Mich., 1978), IEEE Computer Society, 1978, pp. 143\u2013150.","DOI":"10.1109\/SFCS.1978.21"},{"key":"3_CR20","unstructured":"\u2014 The nondeterministic complexity of finite automata, in Mots, M. Lothaire ed., Herm\u00e8s, 1990, pp. 384\u2013400."},{"key":"3_CR21","unstructured":"U. Zimmermann, Linear and Combinatorial Optimization in Ordered Algebraic Structures, Annals of Discrete Mathematics 10, North-Holland, 1981."}],"container-title":["Lecture Notes in Computer Science","Foundations of Software Science and Computation Structures"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-45315-6_3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,5]],"date-time":"2019-05-05T13:09:56Z","timestamp":1557061796000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-45315-6_3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001]]},"ISBN":["9783540418641","9783540453154"],"references-count":21,"URL":"https:\/\/doi.org\/10.1007\/3-540-45315-6_3","relation":{},"ISSN":["0302-9743"],"issn-type":[{"type":"print","value":"0302-9743"}],"subject":[],"published":{"date-parts":[[2001]]}}}