Universal computation and other capabilities of hybrid and continuous dynamical systems
Theoretical Computer Science - Special issue on hybrid systems
ACM Transactions on Programming Languages and Systems (TOPLAS)
Achilles and the tortoise climbing up the arithmetical hierarchy
Journal of Computer and System Sciences - Fourteenth ACM SIGACT-SIGMOD-SIGART symposium on principles of database systems
Dynamic Logic
The Impressive Power of Stopwatches
CONCUR '00 Proceedings of the 11th International Conference on Concurrency Theory
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Computability and completeness in logics of programs (Preliminary Report)
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
Predicate abstraction for reachability analysis of hybrid systems
ACM Transactions on Embedded Computing Systems (TECS)
Matching Explicit and Modal Reasoning about Programs: A Proof Theoretic Delineation of Dynamic Logic
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
Optimal Semicomputable Approximations to Reachable and Invariant Sets
Theory of Computing Systems
Abstractions for hybrid systems
Formal Methods in System Design
Semantical consideration on floyo-hoare logic
SFCS '76 Proceedings of the 17th Annual Symposium on Foundations of Computer Science
Differential Dynamic Logic for Hybrid Systems
Journal of Automated Reasoning
Reachability Analysis of Hybrid Systems Using Support Functions
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
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
Reachability analysis of nonlinear systems using conservative approximation
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
Logical Analysis of Hybrid Systems: Proving Theorems for Complex Dynamics
Logical Analysis of Hybrid Systems: Proving Theorems for Complex Dynamics
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Taylor approximation for hybrid systems
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
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
Hyperstream processing systems: nonstandard modeling of continuous-time signals
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
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Hybrid systems are a fusion of continuous dynamical systems and discrete dynamical systems. They freely combine dynamical features from both worlds. For that reason, it has often been claimed that hybrid systems are more challenging than continuous dynamical systems and than discrete systems. We now show that, proof-theoretically, this is not the case. We present a complete proof-theoretical alignment that interreduces the discrete dynamics and the continuous dynamics of hybrid systems. We give a sound and complete axiomatization of hybrid systems relative to continuous dynamical systems and a sound and complete axiomatization of hybrid systems relative to discrete dynamical systems. Thanks to our axiomatization, proving properties of hybrid systems is exactly the same as proving properties of continuous dynamical systems and again, exactly the same as proving properties of discrete dynamical systems. This fundamental cornerstone sheds light on the nature of hybridness and enables flexible and provably perfect combinations of discrete reasoning with continuous reasoning that lift to all aspects of hybrid systems and their fragments.