{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T16:24:20Z","timestamp":1762100660929},"publisher-location":"Berlin, Heidelberg","reference-count":22,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540714927"},{"type":"electronic","value":"9783540714934"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"DOI":"10.1007\/978-3-540-71493-4_37","type":"book-chapter","created":{"date-parts":[[2007,5,30]],"date-time":"2007-05-30T17:33:57Z","timestamp":1180546437000},"page":"473-486","source":"Crossref","is-referenced-by-count":47,"title":["The Image Computation Problem in Hybrid Systems Model Checking"],"prefix":"10.1007","author":[{"given":"Andr\u00e9","family":"Platzer","sequence":"first","affiliation":[]},{"given":"Edmund M.","family":"Clarke","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"37_CR1","volume-title":"Model Checking","author":"E.M. Clarke","year":"1999","unstructured":"Clarke, E.M., Grumberg, O., Peled, D.A.: Model Checking. MIT Press, Cambridge (1999)"},{"key":"37_CR2","doi-asserted-by":"crossref","DOI":"10.1525\/9780520348097","volume-title":"A Decision Method for Elementary Algebra and Geometry","author":"A. Tarski","year":"1951","unstructured":"Tarski, A.: A Decision Method for Elementary Algebra and Geometry, 2nd edn. University of California Press, Berkeley (1951)","edition":"2"},{"key":"37_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"126","DOI":"10.1007\/3-540-48168-0_10","volume-title":"Computer Science Logic","author":"M. Fr\u00e4nzle","year":"1999","unstructured":"Fr\u00e4nzle, M.: Analysis of hybrid systems. In: Flum, J., Rodr\u00edguez-Artalejo, M. (eds.) CSL 1999. LNCS, vol.\u00a01683, pp. 126\u2013140. Springer, Heidelberg (1999)"},{"key":"37_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1007\/3-540-48983-5_15","volume-title":"Hybrid Systems: Computation and Control","author":"G. Lafferriere","year":"1999","unstructured":"Lafferriere, G., Pappas, G.J., Yovine, S.: A new class of decidable hybrid systems. In: Vaandrager, F.W., van Schuppen, J.H. (eds.) HSCC 1999. LNCS, vol.\u00a01569, pp. 137\u2013151. Springer, Heidelberg (1999)"},{"key":"37_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1007\/3-540-45351-2_9","volume-title":"Hybrid Systems: Computation and Control","author":"H. Anai","year":"2001","unstructured":"Anai, H., Weispfenning, V.: Reach set computations using real quantifier elimination. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A.L. (eds.) HSCC 2001. LNCS, vol.\u00a02034, pp. 63\u201376. Springer, Heidelberg (2001)"},{"key":"37_CR6","series-title":"Lecture Notes in Computer Science","volume-title":"Computer Aided Verification","author":"C. Piazza","year":"2005","unstructured":"Piazza, C., et al.: Algorithmic algebraic model checking I: Challenges from systems biology. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol.\u00a03576, Springer, Heidelberg (2005)"},{"key":"37_CR7","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0701-6","volume-title":"Complexity and real computation","author":"L. Blum","year":"1998","unstructured":"Blum, L., et al.: Complexity and real computation. Springer, New York (1998)"},{"key":"37_CR8","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781107340954","volume-title":"Solving Polynomial Equation Systems II","author":"T. Mora","year":"2005","unstructured":"Mora, T.: Solving Polynomial Equation Systems II. Cambridge Univ. Press, Cambridge (2005)"},{"issue":"4","key":"37_CR9","doi-asserted-by":"publisher","first-page":"509","DOI":"10.1109\/9.664154","volume":"43","author":"C. Tomlin","year":"1998","unstructured":"Tomlin, C., Pappas, G.J., Sastry, S.: Conflict resolution for air traffic management. IEEE Transactions on Automatic Control\u00a043(4), 509\u2013521 (1998)","journal-title":"IEEE Transactions on Automatic Control"},{"key":"37_CR10","first-page":"270","volume-title":"ICECCS","author":"M. Massink","year":"2001","unstructured":"Massink, M., Francesco, N.D.: Modelling free flight with collision avoidance. In: ICECCS, pp. 270\u2013280. IEEE Computer Society Press, Los Alamitos (2001)"},{"issue":"3","key":"37_CR11","doi-asserted-by":"publisher","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. Software Eng.\u00a022(3), 181\u2013201 (1996)","journal-title":"IEEE Trans. Software Eng."},{"key":"37_CR12","doi-asserted-by":"crossref","unstructured":"Silva, B.I., et al.: Modeling and verification of hybrid dynamical system using CheckMate. In: ADPM (2000)","DOI":"10.1109\/ACC.2000.879487"},{"key":"37_CR13","series-title":"Lecture Notes in Computer Science","volume-title":"Hybrid Systems: Computation and Control","author":"G. Frehse","year":"2005","unstructured":"Frehse, G.: PHAVer: Algorithmic verification of hybrid systems past HyTech. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol.\u00a03414, Springer, Heidelberg (2005)"},{"key":"37_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","DOI":"10.1007\/11562948_10","volume-title":"Automated Technology for Verification and Analysis","author":"W. Damm","year":"2005","unstructured":"Damm, W., Pinto, G., Ratschan, S.: Guaranteed termination in the verification of LTL properties of non-linear robust discrete time hybrid systems. In: Peled, D.A., Tsay, Y.-K. (eds.) ATVA 2005. LNCS, vol.\u00a03707, Springer, Heidelberg (2005)"},{"key":"37_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"402","DOI":"10.1007\/978-3-540-31954-2_26","volume-title":"Hybrid Systems: Computation and Control","author":"R. Lanotte","year":"2005","unstructured":"Lanotte, R., Tini, S.: Taylor approximation for hybrid systems. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol.\u00a03414, pp. 402\u2013416. Springer, Heidelberg (2005)"},{"key":"37_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"154","DOI":"10.1007\/10722167_15","volume-title":"Computer Aided Verification","author":"E.M. Clarke","year":"2000","unstructured":"Clarke, E.M., et al.: Counterexample-guided abstraction refinement. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol.\u00a01855, pp. 154\u2013169. Springer, Heidelberg (2000)"},{"key":"37_CR17","doi-asserted-by":"publisher","first-page":"167","DOI":"10.2307\/3029750","volume":"21","author":"M.H. Stone","year":"1948","unstructured":"Stone, M.H.: The generalised Weierstrass approximation theorem. Math. Mag.\u00a021, 167\u2013184 and 237\u2013254 (1948)","journal-title":"Math. Mag."},{"key":"37_CR18","unstructured":"Bejancu, A.: The uniform convergence of multivariate natural splines. Technical Report NA1997\/07, Applied Mathematics, Cambridge, UK (1997)"},{"key":"37_CR19","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-017-2378-7","volume-title":"Multivariate Spline Functions and Their Applications","author":"R.-H. Wang","year":"2001","unstructured":"Wang, R.-H.: Multivariate Spline Functions and Their Applications. Kluwer Academic Publishers, Dordrecht (2001)"},{"key":"37_CR20","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-21738-3","volume-title":"Introduction to Numerical Analysis","author":"J. Stoer","year":"2002","unstructured":"Stoer, J., Bulirsch, R.: Introduction to Numerical Analysis. Springer, New York (2002)"},{"key":"37_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1007\/3-540-36580-X_5","volume-title":"Hybrid Systems: Computation and Control","author":"E. Asarin","year":"2003","unstructured":"Asarin, E., Dang, T., Girard, A.: Reachability analysis of nonlinear systems using conservative approximation. In: Maler, O., Pnueli, A. (eds.) HSCC 2003. LNCS, vol.\u00a02623, pp. 20\u201335. Springer, Heidelberg (2003)"},{"key":"37_CR22","series-title":"Lecture Notes in Computer Science","volume-title":"Hybrid Systems: Computation and Control","year":"2005","unstructured":"Morari, M., Thiele, L. (eds.): HSCC 2005. LNCS, vol.\u00a03414. Springer, Heidelberg (2005)"}],"container-title":["Lecture Notes in Computer Science","Hybrid Systems: Computation and Control"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-71493-4_37.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,8,14]],"date-time":"2021-08-14T06:53:29Z","timestamp":1628924009000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-71493-4_37"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[null]]},"ISBN":["9783540714927","9783540714934"],"references-count":22,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-71493-4_37","relation":{},"subject":[]}}