The algorithmic analysis of hybrid systems
Theoretical Computer Science - Special issue on hybrid systems
Asymptotic Optimization of a Nonlinear Hybrid System Governed by a Markov Decision Process
SIAM Journal on Control and Optimization
Probabilistic simulations for probabilistic processes
Nordic Journal of Computing
Decidable Model Checking of Probabilistic Hybrid Automata
FTRTFT '00 Proceedings of the 6th International Symposium on Formal Techniques in Real-Time and Fault-Tolerant Systems
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Predicate abstraction for reachability analysis of hybrid systems
ACM Transactions on Embedded Computing Systems (TECS)
Analysis of Hybrid Systems Using HySAT
ICONS '08 Proceedings of the Third International Conference on Systems
Probabilistic reachability and safety for controlled discrete time stochastic hybrid systems
Automatica (Journal of IFAC)
Nondeterministic Labeled Markov Processes: Bisimulations and Logical Characterization
QEST '09 Proceedings of the 2009 Sixth International Conference on the Quantitative Evaluation of Systems
A framework for verification of software with time and probabilities
FORMATS'10 Proceedings of the 8th international conference on Formal modeling and analysis of timed systems
Bisimulations for non-deterministic labelled markov processes
Mathematical Structures in Computer Science
Safety verification for probabilistic hybrid systems
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
PARAM: a model checker for parametric markov models
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
PHAVer: algorithmic verification of hybrid systems past hytech
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Rewarding probabilistic hybrid automata
Proceedings of the 16th international conference on Hybrid systems: computation and control
A compositional modelling and analysis framework for stochastic hybrid systems
Formal Methods in System Design
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Dealing with the interplay of randomness and continuous time is important for the formal verification of many real systems. Considering both facets is especially important for wireless sensor networks, distributed control applications, and many other systems of growing importance. An important traditional design and verification goal for such systems is to ensure that unsafe states can never be reached. In the stochastic setting, this translates to the question whether the probability to reach unsafe states remains tolerable. In this paper, we consider stochastic hybrid systems where the continuous-time behaviour is given by differential equations, as for usual hybrid systems, but the targets of discrete jumps are chosen by probability distributions. These distributions may be general measures on state sets. Also non-determinism is supported, and the latter is exploited in an abstraction and evaluation method that establishes safe upper bounds on reachability probabilities. To arrive there requires us to solve semantic intricacies as well as practical problems. In particular, we show that measurability of a complete system follows from the measurability of its constituent parts. On the practical side, we enhance tool support to work effectively on such general models. Experimental evidence is provided demonstrating the applicability of our approach on three case studies, tackled using a prototypical implementation.