Logical Verification and Systematic Parametric Analysis in Train Control
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
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
A Constraint Sequent Calculus for First-Order Logic with Linear Integer Arithmetic
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Computing differential invariants of hybrid systems as fixedpoints
Formal Methods in System Design
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
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
Automatic invariant generation for hybrid systems using ideal fixed points
Proceedings of the 13th ACM international conference on Hybrid systems: computation and control
Switching logic synthesis for reachability
EMSOFT '10 Proceedings of the tenth ACM international conference on Embedded software
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
APLAS'10 Proceedings of the 8th Asian conference on Programming languages and systems
Automatic abstraction of non-linear systems using change of bases transformations
Proceedings of the 14th international conference on Hybrid systems: computation and control
Programming with infinitesimals: a WHILE-language for hybrid system modeling
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Logic and compositional verification of hybrid systems
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
Formal verification of hybrid systems
EMSOFT '11 Proceedings of the ninth ACM international conference on Embedded software
Rigorous discretization of hybrid systems using process calculi
FORMATS'11 Proceedings of the 9th international conference on Formal modeling and analysis of timed systems
Differential dynamic logics: automated theorem proving for hybrid systems
Differential dynamic logics: automated theorem proving for hybrid systems
ICFEM'11 Proceedings of the 13th international conference on Formal methods and software engineering
Distributed theorem proving for distributed hybrid systems
ICFEM'11 Proceedings of the 13th international conference on Formal methods and software engineering
Towards Formal Verification of Freeway Traffic Control
ICCPS '12 Proceedings of the 2012 IEEE/ACM Third International Conference on Cyber-Physical Systems
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
An assume/guarantee based compositional calculus for hybrid CSP
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
Playing hybrid games with keymaera
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
The Complete Proof Theory of Hybrid Systems
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
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
Certifying the safe design of a virtual fixture control algorithm for a surgical robot
Proceedings of the 16th international conference on Hybrid systems: computation and control
Probabilistic program analysis with martingales
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
Time-aware relational abstractions for hybrid systems
Proceedings of the Eleventh ACM International Conference on Embedded Software
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Hybrid systems are models for complex physical systems and are defined as dynamical systems with interacting discrete transitions and continuous evolutions along differential equations. With the goal of developing a theoretical and practical foundation for deductive verification of hybrid systems, we introduce a dynamic logic for hybrid programs, which is a program notation for hybrid systems. As a verification technique that is suitable for automation, we introduce a free variable proof calculus with a novel combination of real-valued free variables and Skolemisation for lifting quantifier elimination for real arithmetic to dynamic logic. The calculus is compositional, i.e., it reduces properties of hybrid programs to properties of their parts. Our main result proves that this calculus axiomatises the transition behaviour of hybrid systems completely relative to differential equations. In a case study with cooperating traffic agents of the European Train Control System, we further show that our calculus is well-suited for verifying realistic hybrid systems with parametric system dynamics.