{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T11:46:11Z","timestamp":1762429571034,"version":"3.28.0"},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2024,8,10]],"date-time":"2024-08-10T00:00:00Z","timestamp":1723248000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,8,10]],"date-time":"2024-08-10T00:00:00Z","timestamp":1723248000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Theory Comput Syst"],"published-print":{"date-parts":[[2024,10]]},"DOI":"10.1007\/s00224-024-10191-x","type":"journal-article","created":{"date-parts":[[2024,8,10]],"date-time":"2024-08-10T01:02:06Z","timestamp":1723251726000},"page":"1427-1441","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Max-plus Algebraic Description of Evolutions of Weighted Timed Event Graphs"],"prefix":"10.1007","volume":"68","author":[{"given":"Kensuke","family":"Kitai","sequence":"first","affiliation":[]},{"given":"Yuki","family":"Nishida","sequence":"additional","affiliation":[]},{"given":"Yoshihide","family":"Watanabe","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,8,10]]},"reference":[{"key":"10191_CR1","doi-asserted-by":"publisher","first-page":"1235","DOI":"10.1109\/PROC.1987.13876","volume":"75","author":"EA Lee","year":"1987","unstructured":"Lee, E.A., Messerschmitt, D.G.: Synchronous data flow. Proc. IEEE 75, 1235\u20131245 (1987). https:\/\/doi.org\/10.1109\/PROC.1987.13876","journal-title":"Proc. IEEE"},{"key":"10191_CR2","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1016\/0166-218X(94)00126-X","volume":"64","author":"A Munier","year":"1996","unstructured":"Munier, A.: The basic cyclic scheduling problem with linear precedence constraints. Discrete Appl. Math. 64, 219\u2013238 (1996). https:\/\/doi.org\/10.1016\/0166-218X(94)00126-X","journal-title":"Discrete Appl. Math."},{"key":"10191_CR3","doi-asserted-by":"publisher","unstructured":"Nakamura, M., Silva, M.: Cycle time computation in deterministically timed weighted marked graphs. In: 1999 7th IEEE International Conference on Emerging Technologies and Factory Automation. Proceedings ETFA\u201999, vol. 2, pp. 1037\u20131046. Barcelona (1999). https:\/\/doi.org\/10.1109\/ETFA.1999.813105","DOI":"10.1109\/ETFA.1999.813105"},{"key":"10191_CR4","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1007\/s10626-007-0035-y","volume":"18","author":"O Marchetti","year":"2008","unstructured":"Marchetti, O., Munier-Kordon, A.: Minimizing place capacities of weighted event graphs for enforcing liveness. Discrete Event Dyn. Syst. 18, 91\u2013109 (2008). https:\/\/doi.org\/10.1007\/s10626-007-0035-y","journal-title":"Discrete Event Dyn. Syst."},{"key":"10191_CR5","doi-asserted-by":"publisher","first-page":"532","DOI":"10.1016\/j.ejor.2008.07.037","volume":"197","author":"O Marchetti","year":"2009","unstructured":"Marchetti, O., Munier-Kordon, A.: A sufficient condition for the liveness of weighted event graphs. Eur. J. Oper. Res. 197, 532\u2013540 (2009). https:\/\/doi.org\/10.1016\/j.ejor.2008.07.037","journal-title":"Eur. J. Oper. Res."},{"key":"10191_CR6","doi-asserted-by":"publisher","first-page":"166","DOI":"10.1016\/j.disopt.2010.03.006","volume":"7","author":"O Marchetti","year":"2010","unstructured":"Marchetti, O., Munier-Kordon, A.: Complexity results for weighted timed event graphs. Discrete Optim. 7, 166\u2013180 (2010). https:\/\/doi.org\/10.1016\/j.disopt.2010.03.006","journal-title":"Discrete Optim."},{"key":"10191_CR7","doi-asserted-by":"publisher","first-page":"1084","DOI":"10.1109\/TASE.2015.2490538","volume":"14","author":"Z He","year":"2017","unstructured":"He, Z., Li, Z., Guia, A.: Optimization of deterministic timed weighted marked graphs. IEEE Trans. Autom. Sci. Eng. 14, 1084\u20131095 (2017). https:\/\/doi.org\/10.1109\/TASE.2015.2490538","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"key":"10191_CR8","doi-asserted-by":"publisher","first-page":"2573","DOI":"10.1109\/TAC.2017.2766202","volume":"63","author":"Z He","year":"2018","unstructured":"He, Z., Li, Z., Guia, A.: Performance optimization for timed weighted marked graphs under infinite server semantics. IEEE Trans. Autom. Contr. 63, 2573\u20132580 (2018). https:\/\/doi.org\/10.1109\/TAC.2017.2766202","journal-title":"IEEE Trans. Autom. Contr."},{"key":"10191_CR9","volume-title":"Synchronization and Linearity","author":"F Baccelli","year":"1992","unstructured":"Baccelli, F., Cohen, G., Olsder, G.J., Quadrat, J.P.: Synchronization and Linearity. Wiley, Chichester (1992)"},{"key":"10191_CR10","doi-asserted-by":"publisher","unstructured":"de Groote, R., Kupar, J., Broersma, H., Smit, G.J.M.: Max-plus algebraic throughput analysis of synchronous dataflow graphs. In: 2012 38th Euromicro Conference on Software Engineering and Advanced Applications, Cesme, pp. 29\u201338 (2012). https:\/\/doi.org\/10.1109\/SEAA.2012.20","DOI":"10.1109\/SEAA.2012.20"},{"key":"10191_CR11","doi-asserted-by":"publisher","unstructured":"Smith, S.E.: Reduction techniques for synchronous dataflow graphs. In: 2009 46th ACM\/IEEE Design Automation Conference, San Francisco, pp. 911\u2013916 (2006). https:\/\/doi.org\/10.1145\/1629911.1630146","DOI":"10.1145\/1629911.1630146"},{"key":"10191_CR12","doi-asserted-by":"publisher","first-page":"1219","DOI":"10.1109\/TAC.2013.2294822","volume":"59","author":"B Cottenceau","year":"2014","unstructured":"Cottenceau, B., Hardouin, L., Boimond, J.L.: Modeling and control of weight-balanced timed event graphs in dioids. IEEE Trans. Autom. Contr. 59, 1219\u20131231 (2014). https:\/\/doi.org\/10.1109\/TAC.2013.2294822","journal-title":"IEEE Trans. Autom. Contr."},{"key":"10191_CR13","doi-asserted-by":"publisher","first-page":"501","DOI":"10.1016\/j.ifacol.2021.04.046","volume":"53","author":"J Trunk","year":"2020","unstructured":"Trunk, J., Schafaschek, G., Cottenceau, B., Hardouin, L., Raisch, J.: Observer for weighted timed event graphs. IFAC-Papers On Line 53, 501\u2013507 (2020). https:\/\/doi.org\/10.1016\/j.ifacol.2021.04.046","journal-title":"IFAC-Papers On Line"},{"key":"10191_CR14","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-84996-299-5","volume-title":"Max-linear Systems: Theory and Algorithms","author":"P Butkovi\u010d","year":"2010","unstructured":"Butkovi\u010d, P.: Max-linear Systems: Theory and Algorithms. Springer, London (2010)"},{"key":"10191_CR15","doi-asserted-by":"publisher","DOI":"10.1515\/9781400865239","volume-title":"Max Plus at Work: Modeling and Analysis of Synchronized Systems: A Course on Max-plus Algebra and Its Applications","author":"B Heidergott","year":"2005","unstructured":"Heidergott, B., Olsder, G.J., van der Woude, J.: Max Plus at Work: Modeling and Analysis of Synchronized Systems: A Course on Max-plus Algebra and Its Applications. Princeton University Press, Princeton (2005)"},{"key":"10191_CR16","doi-asserted-by":"crossref","unstructured":"Gondran, M.: Path algebra and algorithms. In: Roy, B. (ed.) Combinatorial Programming: Methods and Applications. NATO Advanced Study Institutes Series, Series C \u2013 Mathematical and Physical Sciences, vol. 19. Springer, Dordrecht (1975)","DOI":"10.1007\/978-94-011-7557-9_6"},{"key":"10191_CR17","doi-asserted-by":"publisher","first-page":"210","DOI":"10.1109\/TAC.1985.1103925","volume":"AC\u201330","author":"G Cohen","year":"1985","unstructured":"Cohen, G., Dubois, D., Quadrat, J.P., Viot, M.: A linear-system-theoretic view of discrete-event processes and its use for performance evaluation in manufacturing. IEEE Trans. Autom. Contr. AC\u201330, 210\u2013220 (1985). https:\/\/doi.org\/10.1109\/TAC.1985.1103925","journal-title":"IEEE Trans. Autom. Contr."}],"container-title":["Theory of Computing Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00224-024-10191-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00224-024-10191-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00224-024-10191-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,25]],"date-time":"2024-10-25T09:56:22Z","timestamp":1729850182000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00224-024-10191-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,10]]},"references-count":17,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2024,10]]}},"alternative-id":["10191"],"URL":"https:\/\/doi.org\/10.1007\/s00224-024-10191-x","relation":{},"ISSN":["1432-4350","1433-0490"],"issn-type":[{"type":"print","value":"1432-4350"},{"type":"electronic","value":"1433-0490"}],"subject":[],"published":{"date-parts":[[2024,8,10]]},"assertion":[{"value":"25 July 2024","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 August 2024","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no relevant financial or non-financial interests to disclose.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of Interest\/Competing Interests"}}]}}