Partial Cylindrical Algebraic Decomposition for quantifier elimination
Journal of Symbolic Computation
First-order logic and automated theorem proving (2nd ed.)
First-order logic and automated theorem proving (2nd ed.)
A formal description of hybrid systems
Proceedings of the DIMACS/SYCON workshop on Hybrid systems III : verification and control: verification and control
ACM Transactions on Programming Languages and Systems (TOPLAS)
First-order modal logic
Dynamic Logic
Dynamic Input/Output Automata: A Formal Model for Dynamic Systems
CONCUR '01 Proceedings of the 12th International Conference on Concurrency Theory
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Differential Dynamic Logic for Hybrid Systems
Journal of Automated Reasoning
Differential-algebraic Dynamic Logic for Differential-algebraic Programs
Journal of Logic and Computation
Sequential, parallel, and quantified updates of first-order structures
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
R-Charon, a modeling language for reconfigurable hybrid systems
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Specification and analysis of distributed object-based stochastic hybrid systems
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Dynamic logic with non-rigid functions: a basis for object-oriented program verification
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Quantified differential invariants
Proceedings of the 14th international conference on Hybrid systems: computation and control
Adaptive cruise control: hybrid, distributed, and now formally verified
FM'11 Proceedings of the 17th international conference on Formal methods
Stochastic differential dynamic logic for stochastic hybrid programs
CADE'11 Proceedings of the 23rd international conference on Automated deduction
Logic and compositional verification of hybrid systems
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
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
ICCPS '12 Proceedings of the 2012 IEEE/ACM Third International Conference on Cyber-Physical Systems
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
A small model theorem for rectangular hybrid automata networks
FMOODS'12/FORTE'12 Proceedings of the 14th joint IFIP WG 6.1 international conference and Proceedings of the 32nd IFIP WG 6.1 international conference on Formal Techniques for Distributed Systems
Formal verification of distributed aircraft controllers
Proceedings of the 16th international conference on Hybrid systems: computation and control
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
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We address a fundamental mismatch between the combinations of dynamics that occur in complex physical systems and the limited kinds of dynamics supported in analysis. Modern applications combine communication, computation, and control. They may even form dynamic networks, where neither structure nor dimension stay the same while the system follows mixed discrete and continuous dynamics. We provide the logical foundations for closing this analytic gap. We develop a system model for distributed hybrid systems that combines quantified differential equations with quantified assignments and dynamic dimensionality-changes. We introduce a dynamic logic for verifying distributed hybrid systems and present a proof calculus for it. We prove that this calculus is a sound and complete axiomatization of the behavior of distributed hybrid systems relative to quantified differential equations. In our calculus we have proven collision freedom in distributed car control even when new cars may appear dynamically on the road.