Ergodic Control of Switching Diffusions
SIAM Journal on Control and Optimization
Towars a Theory of Stochastic Hybrid Systems
HSCC '00 Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control
Complete Proof Systems for First Order Interval Temporal Logic
LICS '95 Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science
Machine Learning
Numerical vs. statistical probabilistic model checking
International Journal on Software Tools for Technology Transfer (STTT)
Symbolic model checking for probabilistic timed automata
Information and Computation
Semantical consideration on floyo-hoare logic
SFCS '76 Proceedings of the 17th Annual Symposium on Foundations of Computer Science
Probabilistic reachability and safety for controlled discrete time stochastic hybrid systems
Automatica (Journal of IFAC)
Differential-algebraic Dynamic Logic for Differential-algebraic Programs
Journal of Logic and Computation
Bayesian statistical model checking with application to Simulink/Stateflow verification
Proceedings of the 13th ACM international conference on Hybrid systems: computation and control
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
Specification and analysis of distributed object-based stochastic hybrid systems
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Assume-Guarantee verification for probabilistic systems
TACAS'10 Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Computational Methods for Verification of Stochastic Hybrid Systems
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
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
Playing hybrid games with keymaera
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
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
Rewarding probabilistic hybrid automata
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
Bayesian statistical model checking with application to Stateflow/Simulink verification
Formal Methods in System Design
A compositional modelling and analysis framework for stochastic hybrid systems
Formal Methods in System Design
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Logic is a powerful tool for analyzing and verifying systems, including programs, discrete systems, real-time systems, hybrid systems, and distributed systems. Some applications also have a stochastic behavior, however, either because of fundamental properties of nature, uncertain environments, or simplifications to overcome complexity. Discrete probabilistic systems have been studied using logic. But logic has been chronically underdeveloped in the context of stochastic hybrid systems, i.e., systems with interacting discrete, continuous, and stochastic dynamics. We aim at overcoming this deficiency and introduce a dynamic logic for stochastic hybrid systems. Our results indicate that logic is a promising tool for understanding stochastic hybrid systems and can help taming some of their complexity. We introduce a compositional model for stochastic hybrid systems. We prove adaptivity, càdlàg, and Markov time properties, and prove that the semantics of our logic is measurable. We present compositional proof rules, including rules for stochastic differential equations, and prove soundness.