{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T00:05:04Z","timestamp":1725494704134},"publisher-location":"Berlin, Heidelberg","reference-count":22,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540410553"},{"type":"electronic","value":"9783540453529"}],"license":[{"start":{"date-parts":[[2000,1,1]],"date-time":"2000-01-01T00:00:00Z","timestamp":946684800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2000]]},"DOI":"10.1007\/3-540-45352-0_21","type":"book-chapter","created":{"date-parts":[[2007,11,13]],"date-time":"2007-11-13T12:26:02Z","timestamp":1194956762000},"page":"252-263","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Using Cylindrical Algebraic Decomposition for the Analysis of Slope Parametric Hybrid Automata"],"prefix":"10.1007","author":[{"given":"Micha\u00ebl","family":"Ad\u00e9la\u00cfde","sequence":"first","affiliation":[]},{"given":"Olivier","family":"Roux","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2002,1,22]]},"reference":[{"key":"21_CR1","unstructured":"R. Alur, C. Courcoubetis, and D. Dill. Model-checking for real-time systems. In Proc. of the 5th. Annual Symposium on Logic in Computer Science, LICS\u201990, pages 41\u2013425. IEEE Computer Society Press, 1990."},{"key":"21_CR2","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/0304-3975(94)00202-T","volume":"138","author":"R. Alur","year":"1995","unstructured":"R. Alur, C. Courcoubetis, N. Halbwachs, T. A. Henzinger, P-H. Ho, X. Nicollin, A. Olivero, J. Sifakis, and S. Yovine. The algorithmic analysis of hybrid systems. Theoretical Computer Science, 138:3\u201334, 1995.","journal-title":"Theoretical Computer Science"},{"key":"21_CR3","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1016\/0304-3975(94)90010-8","volume":"126","author":"R. Alur","year":"1994","unstructured":"R. Alur and D. Dill. A theory of timed automata. Theoretical Computer Science, 126:183\u2013235, 1994.","journal-title":"Theoretical Computer Science"},{"key":"21_CR4","unstructured":"e99]_M. Ad\u00e9la\u00cfde. Application des bases de gr\u00f6bner \u00e0 l\u2019analyse param\u00e9trique des syst\u00e8mes hybrides. Master\u2019s thesis, Ecole Centrale de Nantes, august 1999."},{"key":"21_CR5","doi-asserted-by":"crossref","unstructured":"R. Alur and T. A. Henzinger. Real-time system = discrete system + clock variables. In T. Rus and C. Rattray, editors, Theories and Experiences for Real-Time System Development-Papers presented at First AMAST Workshop on Real-Time System Development, pages 1\u201329, Iowa City, Iowa, 1994. World Scientific Publishing. Also available as Cornell University technical report CSD-TR-94-1403.","DOI":"10.1142\/9789812831583_0001"},{"key":"21_CR6","doi-asserted-by":"crossref","unstructured":"R. Alur, T. A. Henzinger, and M. Y. Vardi. Parametric real-time reasoning. In Proc. of the 25th Annual ACM Symposium on Theory of Computing, STOC\u201993, pages 592\u2013601, 1993.","DOI":"10.1145\/167088.167242"},{"key":"21_CR7","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1016\/0304-3975(94)00228-B","volume":"138","author":"E. Asarin","year":"1995","unstructured":"E. Asarin, O. Maler, and A. Pnueli. Reachability analysis of dynamical systems having piecewise-constant derivatives. Theoretical Computer Science, 138:35\u201365, 1995.","journal-title":"Theoretical Computer Science"},{"key":"21_CR8","unstructured":"A. Burgue\u00f1o Arajona. V\u00e9rification des Syst\u00e8mes Temporis\u00e9s par des M\u00e9thodes d\u2019Observation et d\u2019Analyse Param\u00e9trique. PhD thesis, Ecole Nationale Sup\u00e9rieure de l\u2019A\u00e9ronautique et de l\u2019Espace, june 1998."},{"key":"21_CR9","doi-asserted-by":"crossref","unstructured":"F. Boniol, A. Burgue\u00f1o, O. Roux, and V. Rusu. Analysis of slope-parametric hybrid automata. In O. Maler, editor, Proc. of the International Workshop on Real time and Hybrid Systems, HART 97, pages 75\u201380. Springer-Verlag, March 26-28 1997.","DOI":"10.1007\/BFb0014715"},{"key":"21_CR10","series-title":"Lect Notes Comput Sci","volume-title":"Task-system analysis using slope-parametric hybrid automata","author":"A. Burgue\u00f1o","year":"1997","unstructured":"A. Burgue\u00f1o and V. Rusu. Task-system analysis using slope-parametric hybrid automata. In Proc. of the Euro-Par\u201997 Workshop on Real-Time Systems and Constraints, Passau, Germany, August 26-29 1997. Springer-Verlag\u2019s Lecture Notes in Computer Science series No1300."},{"key":"21_CR11","doi-asserted-by":"crossref","unstructured":"B. Buchberger. Gr\u00f6bner Bases: an Algorithmic Method in Polynomial Ideal Theory, pages 184\u2013232. Reidel.","DOI":"10.1007\/978-94-009-5225-6_6"},{"key":"21_CR12","doi-asserted-by":"crossref","unstructured":"T. Becker and V. Weispfenning. Gr\u00f6bner Bases: A Computationnal Approach to Commutative Algebra. Springer Verlag, 1993.","DOI":"10.1007\/978-1-4612-0913-3"},{"key":"21_CR13","unstructured":"A.M. Cohen. Gr\u00f6bner base: a primer. Technical report, Computer Algebra Information Network, Europe, 1996."},{"key":"21_CR14","series-title":"Lect Notes Comput Sci","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1007\/3-540-07407-4_17","volume-title":"Quantifier Elimination for Real Closed Fields by Cylindrical Algebraic Decomposition","author":"G. E. Collins","year":"1975","unstructured":"George E. Collins. Quantifier Elimination for Real Closed Fields by Cylindrical Algebraic Decomposition. In Proceedings of the 2nd GI Conference, volume 33 of Lecture Notes in Computer Science, pages 134\u2013183, Kaiserslautern, 1975. Springer, Berlin."},{"key":"21_CR15","unstructured":"J. Little D. Cox and D. O\u2019Shea. Ideals, Varieties and Algorithms. Springer Verlag, 1992."},{"key":"21_CR16","unstructured":"Laureano Gonzales-Vega, Fabrice Rouillier, Marie-Fran\u00c7oise Roy, and Guadalupe Trujillo. Some Tapas of Computer Algebra. Eindoven University of Technology, a.m. cohen and h. cuypers and h. sterk edition, 1995."},{"key":"21_CR17","unstructured":"T. Henziger. The theroie of hybrid auromata. In IEEE Symposium on Logic In Computer Science, pages 278\u2013282, 1996."},{"key":"21_CR18","series-title":"Lect Notes Comput Sci","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1007\/3-540-60472-3_14","volume-title":"Hybrid Systems II","author":"T.A. Henzinger","year":"1995","unstructured":"T.A. Henzinger and P.-H. Ho. HyTech: The Cornell Hybrid Technology Tool. In P. Antsaklis, A. Nerode, W. Kohn, and S. Sastry, editors, Hybrid Systems II, Lecture Notes in Computer Science 999, pages 265\u2013293. Springer-Verlag, 1995."},{"key":"21_CR19","series-title":"Lect Notes Comput Sci","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1007\/BFb0032003","volume-title":"Proc. of the REX workshop \u2018Real-Time: theory in practicers","author":"O. Maler","year":"1992","unstructured":"O. Maler, Z. Manna, and A. Pnueli. From timed to hybrid systems. In J. W. de Bakker, K. Huizing, W.-P. de Roever, and G. Rozenberg, editors, Proc. of the REX workshop \u2018Real-Time: theory in practicers, volume 600 of Lecture Notes in Computer Science, pages 447\u2013484, Berlin, New York, 1992. Springer-Verlag."},{"key":"21_CR20","unstructured":"M. Jirstrand. Cylindrical algebraic decomposition \u2014 an introduction. Technical report, Computer Algebra Information Network, Europe, Departement of Electrical Engineering, Link\u00f6ping university, S-581 83 Link\u00f6ping. Sweden, October 1995."},{"key":"21_CR21","unstructured":"G. Roda. Quantifier elimination \u2014 lecture notes based on a course by g.e. collins, risc-summer semester 96. Technical report, Computer Algebra Information Network, Europe, July 1996."},{"issue":"2","key":"21_CR22","first-page":"131","volume":"130","author":"F. Wang","year":"1996","unstructured":"Farn Wang. Parametric timing analysis for real-time systems. 130(2):131\u2013150, 1 November 1996.","journal-title":"Parametric timing analysis for real-time systems"}],"container-title":["Lecture Notes in Computer Science","Formal Techniques in Real-Time and Fault-Tolerant Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-45352-0_21","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,19]],"date-time":"2019-05-19T10:47:25Z","timestamp":1558262845000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-45352-0_21"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000]]},"ISBN":["9783540410553","9783540453529"],"references-count":22,"URL":"https:\/\/doi.org\/10.1007\/3-540-45352-0_21","relation":{},"ISSN":["0302-9743"],"issn-type":[{"type":"print","value":"0302-9743"}],"subject":[],"published":{"date-parts":[[2000]]},"assertion":[{"value":"22 January 2002","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}