Algebraic laws for nondeterminism and concurrency
Journal of the ACM (JACM)
Applied & computational complex analysis: power series integration conformal mapping location of zero
Bisimulation through probabilistic testing
Information and Computation
Theoretical Computer Science
A compositional approach to performance modelling
A compositional approach to performance modelling
Modeling and verification of randomized distributed real-time systems
Modeling and verification of randomized distributed real-time systems
Model-checking continuous-time Markov chains
ACM Transactions on Computational Logic (TOCL)
Numerical Methods for Scientists and Engineers
Numerical Methods for Scientists and Engineers
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Exploiting Modal Logic to Express Performance Measures
TOOLS '00 Proceedings of the 11th International Conference on Computer Performance Evaluation: Modelling Techniques and Tools
Model-Checking Algorithms for Continuous-Time Markov Chains
IEEE Transactions on Software Engineering
Probabilistic symbolic model checking with PRISM: a hybrid approach
International Journal on Software Tools for Technology Transfer (STTT) - Special section on tools and algorithms for the construction and analysis of systems
QEST '05 Proceedings of the Second International Conference on the Quantitative Evaluation of Systems
An O(nlog/sup 3/ n) algorithm for the real root problem
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Compositional Modeling and Minimization of Time-Inhomogeneous Markov Chains
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Interactive Markov chains: and the quest for quantified quality
Interactive Markov chains: and the quest for quantified quality
Logical characterizations of bisimulations for discrete probabilistic systems
FOSSACS'07 Proceedings of the 10th international conference on Foundations of software science and computational structures
LTL Model Checking of Time-Inhomogeneous Markov Chains
ATVA '09 Proceedings of the 7th International Symposium on Automated Technology for Verification and Analysis
Weighted probabilistic equivalence preserves ω-regular properties
MMB'12/DFT'12 Proceedings of the 16th international GI/ITG conference on Measurement, Modelling, and Evaluation of Computing Systems and Dependability and Fault Tolerance
CONCUR'12 Proceedings of the 23rd international conference on Concurrency Theory
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This paper presents a stochastic variant of Hennessy-Milner logic that is interpreted over (state-labeled) inhomogeneous continuous-time Markov chains (ICTMCs), i.e., Markov chains in which transition rates are functions over time t. For piecewise constant rate functions, the model-checking problem is shown to be reducible to finding the zeros of an exponential polynomial. Using Sturm sequences and Newton's method, we obtain an approximative model-checking algorithm which is linear in the size of the ICTMC, logarithmic in the number of bits precision, and exponential in the nesting depth of the formula.