Partial Cylindrical Algebraic Decomposition for quantifier elimination
Journal of Symbolic Computation
Dynamic Logic
Reach Set Computations Using Real Quantifier Elimination
HSCC '01 Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control
Analysis of Hybrid Systems: An Ounce of Realism Can Save an Infinity of States
CSL '99 Proceedings of the 13th International Workshop and 8th Annual Conference of the EACSL on Computer Science Logic
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Modelling Free Flight with Collision Avoidance
ICECCS '01 Proceedings of the Seventh International Conference on Engineering of Complex Computer Systems
Constructing invariants for hybrid systems
Formal Methods in System Design
Differential Dynamic Logic for Hybrid Systems
Journal of Automated Reasoning
Differential Dynamic Logic for Verifying Parametric Hybrid Systems
TABLEAUX '07 Proceedings of the 16th international conference on Automated Reasoning with Analytic Tableaux and Related Methods
Logical Verification and Systematic Parametric Analysis in Train Control
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Systematic simulation using sensitivity analysis
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
The image computation problem in hybrid systems model checking
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
Reachability analysis of nonlinear systems using conservative approximation
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
ATVA'05 Proceedings of the Third international conference on Automated Technology for Verification and Analysis
Algorithmic algebraic model checking i: challenges from systems biology
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
Generating polynomial invariants for hybrid systems
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Formal Verification of Curved Flight Collision Avoidance Maneuvers: A Case Study
FM '09 Proceedings of the 2nd World Congress on Formal Methods
Generating invariants for non-linear hybrid systems by linear algebraic methods
SAS'10 Proceedings of the 17th international conference on Static analysis
APLAS'10 Proceedings of the 8th Asian conference on Programming languages and systems
Quantified differential invariants
Proceedings of the 14th international conference on Hybrid systems: computation and control
Logic and compositional verification of hybrid systems
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
Computing semi-algebraic invariants for polynomial dynamical systems
EMSOFT '11 Proceedings of the ninth ACM international conference on Embedded software
Formal verification of hybrid systems
EMSOFT '11 Proceedings of the ninth ACM international conference on Embedded software
Specifications for decidable hybrid games
Theoretical Computer Science
Differential dynamic logics: automated theorem proving for hybrid systems
Differential dynamic logics: automated theorem proving for hybrid systems
Transcendental inductive invariants generation for non-linear differential and hybrid systems
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
Verification of Periodically Controlled Hybrid Systems: Application to an Autonomous Vehicle
ACM Transactions on Embedded Computing Systems (TECS) - Special Section on CAPA'09, Special Section on WHS'09, and Special Section VCPSS' 09
Verification of Safety and Liveness Properties of Metric Transition Systems
ACM Transactions on Embedded Computing Systems (TECS) - Special Section on CAPA'09, Special Section on WHS'09, and Special Section VCPSS' 09
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Logical analysis of hybrid systems: a complete answer to a complexity challenge
DCFS'12 Proceedings of the 14th international conference on Descriptional Complexity of Formal Systems
Computation of polytopic invariants for polynomial dynamical systems using linear programming
Automatica (Journal of IFAC)
Exponential-Condition-Based barrier certificate generation for safety verification of hybrid systems
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
Synthesizing switching controllers for hybrid systems by generating invariants
Theories of Programming and Formal Methods
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We introduce a fixedpoint algorithm for verifying safety properties of hybrid systems with differential equations whose right-hand sides are polynomials in the state variables. In order to verify nontrivial systems without solving their differential equations and without numerical errors, we use a continuous generalization of induction, for which our algorithm computes the required differential invariants. As a means for combining local differential invariants into global system invariants in a sound way, our fixedpoint algorithm works with a compositional verification logic for hybrid systems. To improve the verification power, we further introduce a saturation procedurethat refines the system dynamics successively with differential invariants until safety becomes provable. By complementing our symbolic verification algorithm with a robust version of numerical falsification, we obtain a fast and sound verification procedure. We verify roundabout maneuvers in air traffic management and collision avoidance in train control.