Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition, In: Automata Theory and Formal Languages . LNCS, vol.33, pp.134-183, 1975. ,
Partial Cylindrical Algebraic Decomposition for quantifier elimination, Journal of Symbolic Computation, vol.12, issue.3, pp.299-328, 1991. ,
DOI : 10.1016/S0747-7171(08)80152-6
Ideals, Varieties, and Algorithms -an introduction to computational algebraic geometry and commutative algebra, 1997. ,
Mémoire sur leséquationsles´leséquations différentielles algébriques du premier ordre et du premier degré, Bulletin des Sciences Mathématiques et Astronomiques, vol.2, issue.1, pp.151-200, 1878. ,
Simplification of Quantifier-free Formulae over Ordered Fields, Journal of Symbolic Computation, vol.24, issue.2, pp.209-231, 1995. ,
DOI : 10.1006/jsco.1997.0123
Qualitative Theory of Planar Differential Systems, 2006. ,
A new efficient algorithm for computing Gröbner bases without reduction to zero (F5), pp.75-83, 2002. ,
Characterizing Algebraic Invariants by Differential Radical Invariants, In: TACAS, vol.8413, pp.279-294, 2014. ,
DOI : 10.1007/978-3-642-54862-8_19
Invariance of Conjunctions of Polynomial Equalities for Algebraic Differential Equations, In: SAS. LNCS, vol.8723, pp.151-167, 2014. ,
DOI : 10.1007/978-3-319-10936-7_10
A Hierarchy of Proof Rules for Checking Differential Invariance of Algebraic Sets, In: VMCAI. LNCS, vol.8931, pp.431-448, 2015. ,
DOI : 10.1007/978-3-662-46081-8_24
Integrability and Nonintegrability of Dynamical Systems Advanced series in nonlinear dynamics, 2001. ,
VorlesungenüberVorlesungen¨Vorlesungenüber continuierliche Gruppen mit Geometrischen und anderen Anwendungen, 1893. ,
Sur l'application de la méthode des approximations successives auxéquationsaux´auxéquations différentielles ordinaires du premier ordre, Comptes rendus hebdomadaires des séances de l'Académie des sciences, pp.454-458, 1894. ,
Computing semi-algebraic invariants for polynomial dynamical systems, Proceedings of the ninth ACM international conference on Embedded software, EMSOFT '11, pp.97-106, 2011. ,
DOI : 10.1145/2038642.2038659
Generating invariants for nonlinear hybrid systems by linear algebraic methods, In: SAS. LNCS, vol.6337, pp.373-389, 2010. ,
Membership in polynomial ideals over Q is exponential space complete, STACS, pp.400-406, 1989. ,
DOI : 10.1007/BFb0029002
Applications of Lie Groups to Differential Equations, 2000. ,
Differential Dynamic Logic for Hybrid Systems, Journal of Automated Reasoning, vol.30, issue.1, pp.143-189, 2008. ,
DOI : 10.1007/s10817-008-9103-8
Differential-algebraic Dynamic Logic for Differential-algebraic Programs, Journal of Logic and Computation, vol.20, issue.1, pp.309-352, 2010. ,
DOI : 10.1093/logcom/exn070
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.140.2188
A differential operator approach to equational differential invariants -(invited paper), In: ITP. LNCS, vol.7406, pp.28-48, 2012. ,
The Structure of Differential Invariants and Differential Cut Elimination, Logical Methods in Computer Science, vol.8, issue.4, pp.1-38, 2012. ,
DOI : 10.2168/LMCS-8(4:16)2012
Safety Verification of Hybrid Systems Using Barrier Certificates, Hybrid Systems: Computation and Control, pp.477-492, 2004. ,
DOI : 10.1007/978-3-540-24743-2_32
A framework for worst-case and stochastic safety verification using barrier certificates. Automatic Control, IEEE Transactions on, vol.52, issue.8, pp.1415-1428, 2007. ,
Some undecidable problems involving elementary functions of a real variable, The Journal of Symbolic Logic, vol.33, issue.04, pp.514-520, 1968. ,
DOI : 10.2307/1970289
Constructing invariants for hybrid systems, Formal Methods in System Design, vol.96, issue.2, pp.25-55, 2008. ,
DOI : 10.1007/s10703-007-0046-1
Deductive verification of continuous dynamical systems, of LIPIcs, pp.383-394, 2009. ,
A Decision Method for Elementary Algebra and Geometry, Bull. Amer. Math. Soc, vol.59, 1951. ,
DOI : 10.1007/978-3-7091-9459-1_3
Abstractions for hybrid systems, Formal Methods in System Design, vol.92, issue.3, pp.57-83, 2008. ,
DOI : 10.1007/s10703-007-0044-3
Ordinary Differential Equations, 1998. ,
Tangent cone and contingent cone to the intersection of two closed sets. Nonlinear Analysis: Theory, Methods & Applications, vol.73, issue.5, pp.1203-1220, 2010. ,