Differential automata and their discrete simulators
Non-Linear Analysis
Differential equations and dynamical systems
Differential equations and dynamical systems
A classical mind
The algorithmic analysis of hybrid systems
Theoretical Computer Science - Special issue on hybrid systems
General hybrid dynamical systems: modeling, analysis, and control
Proceedings of the DIMACS/SYCON workshop on Hybrid systems III : verification and control: verification and control
A formal description of hybrid systems
Proceedings of the DIMACS/SYCON workshop on Hybrid systems III : verification and control: verification and control
Studies in hybrid systems: modeling, analysis, and control
Studies in hybrid systems: modeling, analysis, and control
ACM Transactions on Programming Languages and Systems (TOPLAS)
Dynamic Logic
Theoretical Computer Science
Hybrid Systems
The Impressive Power of Stopwatches
CONCUR '00 Proceedings of the 11th International Conference on Concurrency Theory
Deductive Verification of Hybrid Systems Using STeP
HSCC '98 Proceedings of the First International Workshop on Hybrid Systems: Computation and Control
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Process algebra for hybrid systems
Theoretical Computer Science - Process algebra
Safety verification of hybrid systems by constraint propagation-based abstraction refinement
ACM Transactions on Embedded Computing Systems (TECS)
PHAVer: algorithmic verification of hybrid systems past HyTech
International Journal on Software Tools for Technology Transfer (STTT)
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
Computing Differential Invariants of Hybrid Systems as Fixedpoints
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
KeYmaera: A Hybrid Theorem Prover for Hybrid Systems (System Description)
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Formal Verification of Curved Flight Collision Avoidance Maneuvers: A Case Study
FM '09 Proceedings of the 2nd World Congress on Formal Methods
European Train Control System: A Case Study in Formal Verification
ICFEM '09 Proceedings of the 11th International Conference on Formal Engineering Methods: Formal Methods and Software Engineering
Differential-algebraic Dynamic Logic for Differential-algebraic Programs
Journal of Logic and Computation
The image computation problem in hybrid systems model checking
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
Verification of object-oriented software: The KeY approach
Verification of object-oriented software: The KeY approach
Logical Analysis of Hybrid Systems: Proving Theorems for Complex Dynamics
Logical Analysis of Hybrid Systems: Proving Theorems for Complex Dynamics
Quantified differential dynamic logic for distributed hybrid systems
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
Quantified differential invariants
Proceedings of the 14th international conference on Hybrid systems: computation and control
Stochastic differential dynamic logic for stochastic hybrid programs
CADE'11 Proceedings of the 23rd international conference on Automated deduction
ATVA'05 Proceedings of the Third international conference on Automated Technology for Verification and Analysis
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Hybrid systems are models for complex physical systems and have become a widely used concept for understanding their behavior. Many applications are safety-critical, including car, railway, and air traffic control, robotics, physical-chemical process control, and biomedical devices. Hybrid systems analysis studies how we can build computerised controllers for physical systems which are guaranteed to meet their design goals. The continuous dynamics of hybrid systems can be modeled by differential equations, the discrete dynamics by a combination of discrete state-transitions and conditional execution. The discrete and continuous dynamics interact to form hybrid systems, which makes them quite challenging for verification. In this tutorial, we survey state-of-the-art verification techniques for hybrid systems. In particular, we focus on a coherent logical approach for systematic hybrid systems analysis. We survey theory, practice, and applications, and show how hybrid systems can be verified in the hybrid systems verification tool KeYmaera. KeYmaera has been used successfully to verify safety, reactivity, controllability, and liveness properties, including collision freedom in air traffic, car, and railway control systems. It has also been used to verify properties of electrical circuits.