{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,23]],"date-time":"2025-04-23T04:17:48Z","timestamp":1745381868695,"version":"3.40.4"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"12","license":[{"start":{"date-parts":[[2012,11,24]],"date-time":"2012-11-24T00:00:00Z","timestamp":1353715200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sci. China Inf. Sci."],"published-print":{"date-parts":[[2012,12]]},"DOI":"10.1007\/s11432-012-4726-0","type":"journal-article","created":{"date-parts":[[2012,11,23]],"date-time":"2012-11-23T17:46:45Z","timestamp":1353692805000},"page":"2663-2674","source":"Crossref","is-referenced-by-count":1,"title":["Loop reduction techniques for reachability analysis of linear hybrid automata"],"prefix":"10.1007","volume":"55","author":[{"given":"MinXue","family":"Pan","sequence":"first","affiliation":[]},{"given":"You","family":"Li","sequence":"additional","affiliation":[]},{"given":"Lei","family":"Bu","sequence":"additional","affiliation":[]},{"given":"XuanDong","family":"Li","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,11,24]]},"reference":[{"key":"4726_CR1","doi-asserted-by":"crossref","unstructured":"Henzinger T A. The theory of hybrid automata. In: Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science, New Brunswick, 1996. 278\u2013292","DOI":"10.1109\/LICS.1996.561342"},{"key":"4726_CR2","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/0304-3975(94)00228-B","volume":"138","author":"E. Asarin","year":"1995","unstructured":"Asarin E, Maler O, Pnueli A. Reachability analysis of dynamical systems having piecewise-constant derivatives. Theor Comput Sci, 1995, 138: 35\u201365","journal-title":"Theor Comput Sci"},{"key":"4726_CR3","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/0304-3975(94)00202-T","volume":"138","author":"R. Alur","year":"1995","unstructured":"Alur R, Courcoubetis C, Halbwachs N, et al. The algorithmic analysis of hybrid systems. Theor Comput Sci, 1995, 138: 3\u201334","journal-title":"Theor Comput Sci"},{"key":"4726_CR4","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1109\/32.489079","volume":"22","author":"R. Alur","year":"1996","unstructured":"Alur R, Henzinger T A, Ho P H. Automatic symbolic verification of embedded systems. IEEE Trans Softw Eng, 1996, 22: 181\u2013201","journal-title":"IEEE Trans Softw Eng"},{"key":"4726_CR5","unstructured":"Silva B I, Richeson K, Krogh B, et al. Modeling and verification of hybrid dynamical system using checkmate. In: Proceedings of the 4th International Conference on Automation of Mixed Processes: Hybrid Dynamic Systems. Dortmund, 2000. 323\u2013328"},{"key":"4726_CR6","series-title":"Lecture Notes in Computer Science","first-page":"746","volume-title":"Computer Aided Verification","author":"E. Asarin","year":"2002","unstructured":"Asarin E, Dang T, Maler O. The d\/dt tool for verification of hybrid systems. In: Brinksma E, Larsen K, eds. Computer Aided Verification. Lecture Notes in Computer Science, Vol 2404. Berlin: Springer, 2002. 746\u2013770"},{"key":"4726_CR7","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1007\/s100090050008","volume":"1","author":"T. A. Henzinger","year":"1997","unstructured":"Henzinger T A, Ho P H, Wong-Toi H. HyTech: A model checker for hybrid systems. Int J Softw Tools Technol Transf, 1997, 1: 110\u2013122","journal-title":"Int J Softw Tools Technol Transf"},{"key":"4726_CR8","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1007\/s10009-007-0062-x","volume":"10","author":"G. Frehse","year":"2008","unstructured":"Frehse G. Phaver: algorithmic verification of hybrid systems past HyTech. Int J Softw Tools Technol Transf, 2008, 10: 263\u2013279","journal-title":"Int J Softw Tools Technol Transf"},{"key":"4726_CR9","first-page":"1582","volume-title":"IEEE International Symposium on Computer Aided Control System Design","author":"E. Asarin","year":"2006","unstructured":"Asarin E, Dang T, Frehse G, et al. Recent progress in continuous and hybrid reachability analysis. In: IEEE International Symposium on Computer Aided Control System Design. Washington, DC: IEEE, 2006. 1582\u20131587"},{"key":"4726_CR10","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1007\/s10703-006-0031-0","volume":"30","author":"M. Fr\u00e4nzle","year":"2007","unstructured":"Fr\u00e4nzle M, Herde C. HySat: An efficient proof engine for bounded model checking of hybrid systems. Form Methods Syst Des, 2007, 30: 179\u2013198","journal-title":"Form Methods Syst Des"},{"key":"4726_CR11","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.entcs.2004.12.022","volume":"119","author":"G. Audemard","year":"2005","unstructured":"Audemard G, Bozzano M, Cimatti A, et al. Verifying industrial hybrid systems with MathSAT. Electron Notes Theor Comput Sci, 2005, 119: 17\u201332","journal-title":"Electron Notes Theor Comput Sci"},{"key":"4726_CR12","unstructured":"Bu L, Li Y, Wang L, et al. BACH: Bounded reachability checker for linear hybrid automata. In: 8th International Conference on Formal Methods in Computer Aided Design, Portland, 2008. 65\u201368"},{"key":"4726_CR13","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1007\/s10009-010-0163-9","volume":"13","author":"L. Bu","year":"2011","unstructured":"Bu L, Li X. Path-oriented bounded reachability analysis of composed linear hybrid systems. Int J Softw Tools Technol Transf, 2011, 13: 307\u2013317","journal-title":"Int J Softw Tools Technol Transf"},{"key":"4726_CR14","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1109\/REAL.1995.495196","volume-title":"16th IEEE Real-Time Systems Symposium","author":"T. A. Henzinger","year":"1995","unstructured":"Henzinger T A, Ho P H, and Wong-Toi H. HyTech: the next generation. In: 16th IEEE Real-Time Systems Symposium. Washington, DC: IEEE, 1995. 56\u201365"},{"key":"4726_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1007\/3-540-46430-1_14","volume-title":"Hybrid Systems: Computation and Control","author":"T. A. Henzinger","year":"2000","unstructured":"Henzinger T A, Horowitz B, Majumdar R, et al. Beyond HyTech: Hybrid systems analysis using interval numerical methods. In: Lynch N, Krogh B, eds. Hybrid Systems: Computation and Control. Lecture Notes in Computer Science, Vol 1790. Berlin: Springer, 2000, 130\u2013144"},{"key":"4726_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1007\/3-540-45789-5_17","volume-title":"Static Analysis","author":"R. Bagnara","year":"2002","unstructured":"Bagnara R, Ricci E, Zaffanella E, et al. Possibly not closed convex polyhedra and the parma polyhedra library. In: Hermenegildo M and Puebla G, eds. Static Analysis. Lecture Notes in Computer Science, Vol 2477. Berlin: Springer, 2002, 213\u2013229"},{"key":"4726_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"482","DOI":"10.1007\/3-540-36580-X_35","volume-title":"Hybrid Systems: Computation and Control","author":"O. Stursberg","year":"2003","unstructured":"Stursberg O, Krogh H. Efficient representation and computation of reachable sets for hybrid systems. In: Maler O, Pnueli A, eds. Hybrid Systems: Computation and Control. Lecture Notes in Computer Science, Vol 2623. Berlin: Springer, 2003. 482\u2013497"},{"key":"4726_CR18","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1007\/3-540-58485-4_43","volume-title":"Static Analysis","author":"N. Halbwachs","year":"1994","unstructured":"Halbwachs N, Proy Y, Raymond P. Verification of linear hybrid systems by means of convex approximations. In: Le Charlier B, ed. Static Analysis. Lecture Notes in Computer Science, Vol 864. Berlin: Springer, 1994. 223\u2013237"},{"key":"4726_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"252","DOI":"10.1007\/3-540-60472-3_13","volume-title":"Hybrid Systems II","author":"T. A. Henzinger","year":"1995","unstructured":"Henzinger T A, Ho P H. A note on abstract interpretation strategies for hybrid automata. In: Antsaklis P, Kohn W, Nerode A, eds. Hybrid Systems II. Lecture Notes in Computer Science, Vol 999. Berlin: Springer, 1995. 252\u2013264"},{"key":"4726_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1007\/3-540-46430-1_6","volume-title":"Hybrid Systems: Computation and Control","author":"E. Asarin","year":"2000","unstructured":"Asarin E, Dang T, Maler O, et al. Approximate reachability analysis of piecewise-linear dynamical systems. In: Lynch N, Krogh B, eds. Hybrid Systems: Computation and Control. Lecture Notes in Computer Science, Vol 1790. Berlin: Springer, 2000. 20\u201331"},{"key":"4726_CR21","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1287\/ijoc.3.2.157","volume":"3","author":"J. W. Chinneck","year":"1991","unstructured":"Chinneck J W, Dravnieks E W. Locating minimal infeasible constraint sets in linear programs. ORSA J Comput, 1991, 3: 157\u2013168","journal-title":"ORSA J Comput"},{"key":"4726_CR22","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1006\/inco.1998.2774","volume":"150","author":"Y. Kesten","year":"1999","unstructured":"Kesten Y, Pnueli A, Sifakis J, et al. Decidable integration graphs. Inf Comput, 1999, 150: 209\u2013243","journal-title":"Inf Comput"},{"key":"4726_CR23","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1023\/A:1008626013578","volume":"11","author":"R. Alur","year":"1997","unstructured":"Alur R, Courcoubetis C, Henzinger T A. Computing accumulated delays in real-time systems. Form Methods Syst Des, 1997, 11: 137\u2013155","journal-title":"Form Methods Syst Des"},{"key":"4726_CR24","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1006\/jcss.1998.1581","volume":"57","author":"T. A. Henzinger","year":"1998","unstructured":"Henzinger T A, Kopke P W, Puri A, et al. What\u2019s decidable about hybrid automata? J Comput Syst Sci, 1998, 57: 94\u2013124","journal-title":"J Comput Syst Sci"},{"key":"4726_CR25","doi-asserted-by":"crossref","unstructured":"Li X, Zhao J, Yu P, et al. Positive loop-closed automata: a decidable class of hybrid systems. J Logic Algebr Program, 2002: 79\u2013108","DOI":"10.1016\/S1567-8326(02)00024-3"},{"key":"4726_CR26","first-page":"73","volume-title":"Proceedings of the 14th International Conference on Hybrid Systems: Computation and Control","author":"W. Damm","year":"2011","unstructured":"Damm W, Ihlemann C, Sofronie-Stokkermans V. Decidability and complexity for the verification of safety properties of reasonable linear hybrid automata. In: Proceedings of the 14th International Conference on Hybrid Systems: Computation and Control. New York: ACM, 2011. 73\u201382"}],"container-title":["Science China Information Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11432-012-4726-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11432-012-4726-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11432-012-4726-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,22]],"date-time":"2025-04-22T17:11:24Z","timestamp":1745341884000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11432-012-4726-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,11,24]]},"references-count":26,"journal-issue":{"issue":"12","published-print":{"date-parts":[[2012,12]]}},"alternative-id":["4726"],"URL":"https:\/\/doi.org\/10.1007\/s11432-012-4726-0","relation":{},"ISSN":["1674-733X","1869-1919"],"issn-type":[{"type":"print","value":"1674-733X"},{"type":"electronic","value":"1869-1919"}],"subject":[],"published":{"date-parts":[[2012,11,24]]}}}