Matrix analysis
The complexity of probabilistic verification
Journal of the ACM (JACM)
Computing Accumulated Delays in Real-time Systems
Formal Methods in System Design - Special issue on computer aided verification (CAV 93)
Information and Computation
Model-checking continuous-time Markov chains
ACM Transactions on Computational Logic (TOCL)
A Laplace transform algorithm for the volume of a convex polytope
Journal of the ACM (JACM)
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Checking Hybrid Automata for Linear Duration Invariants
ASIAN '97 Proceedings of the Third Asian Computing Science Conference on Advances in Computing Science
On the Logical Characterisation of Performability Properties
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
ProCoS Proceedings of the Third International Symposium Organized Jointly with the Working Group Provably Correct Systems on Formal Techniques in Real-Time and Fault-Tolerant Systems
Model Checking Performability Properties
DSN '02 Proceedings of the 2002 International Conference on Dependable Systems and Networks
Model-Checking Algorithms for Continuous-Time Markov Chains
IEEE Transactions on Software Engineering
Using probabilistic model checking for dynamic power management
Formal Aspects of Computing
On Verification of Probabilistic Timed Automata against Probabilistic Duration Properties
RTCSA '07 Proceedings of the 13th IEEE International Conference on Embedded and Real-Time Computing Systems and Applications
Principles of Model Checking (Representation and Mind Series)
Principles of Model Checking (Representation and Mind Series)
Verification of Linear Duration Invariants by Model Checking CTL Properties
Proceedings of the 5th international colloquium on Theoretical Aspects of Computing
Infinite Runs in Weighted Timed Automata with Energy Constraints
FORMATS '08 Proceedings of the 6th international conference on Formal Modeling and Analysis of Timed Systems
Quantitative Model Checking of Continuous-Time Markov Chains Against Timed Automata Specifications
LICS '09 Proceedings of the 2009 24th Annual IEEE Symposium on Logic In Computer Science
Timed automata with observers under energy constraints
Proceedings of the 13th ACM international conference on Hybrid systems: computation and control
SFM'07 Proceedings of the 7th international conference on Formal methods for performance evaluation
Fluid models in performance analysis
SFM'07 Proceedings of the 7th international conference on Formal methods for performance evaluation
Performance evaluation and model checking join forces
Communications of the ACM
Reasoning about QoS Contracts in the Probabilistic Duration Calculus
Electronic Notes in Theoretical Computer Science (ENTCS)
Model Checking Multivariate State Rewards
QEST '10 Proceedings of the 2010 Seventh International Conference on the Quantitative Evaluation of Systems
Efficient CTMC model checking of linear real-time objectives
TACAS'11/ETAPS'11 Proceedings of the 17th international conference on Tools and algorithms for the construction and analysis of systems: part of the joint European conferences on theory and practice of software
PRISM 4.0: verification of probabilistic real-time systems
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
Time-bounded verification of CTMCs against real-time specifications
FORMATS'11 Proceedings of the 9th international conference on Formal modeling and analysis of timed systems
Temporal Specifications with Accumulative Values
LICS '11 Proceedings of the 2011 IEEE 26th Annual Symposium on Logic in Computer Science
Verifying linear duration constraints of timed automata
ICTAC'04 Proceedings of the First international conference on Theoretical Aspects of Computing
Verification of linear duration properties over continuous-time markov chains
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
Stochastic modeling of a power-managed system-construction and optimization
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Hi-index | 0.00 |
Stochastic modelling and algorithmic verification techniques have been proved useful in analysing and detecting unusual trends in performance and energy usage of systems such as power management controllers and wireless sensor devices. Many important properties are dependent on the cumulated time that the device spends in certain states, possibly intermittently. We study the problem of verifying continuous-time Markov Chains (CTMCs) against Linear Duration Properties (LDP), that is, properties stated as conjunctions of linear constraints over the total duration of time spent in states that satisfy a given property. We identify two classes of LDP properties, Eventuality Duration Properties (EDP) and Invariance Duration Properties (IDP), respectively referring to the reachability of a set of goal states, within a time bound; and the continuous satisfaction of a duration property over an execution path. The central question that we address is how to compute the probability of the set of infinite timed paths of the CTMC that satisfy a given LDP. We present algorithms to approximate these probabilities up to a given precision, stating their complexity and error bounds. The algorithms mainly employ an adaptation of uniformisation and the computation of volumes of multidimensional integrals under systems of linear constraints, together with different mechanisms to bound the errors.