Parallel computation for well-endowed rings and space-bounded probabilistic machines
Information and Control
The complexity of elementary algebra and geometry
Journal of Computer and System Sciences
The complexity of Markov decision processes
Mathematics of Operations Research
Some algebraic and geometric computations in PSPACE
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
On the Computational Complexity of Approximating Distributions by Probabilistic Automata
Machine Learning - Computational learning theory
Reasoning about infinite computations
Information and Computation
Complexity and real computation
Complexity and real computation
Reachability Analysis of Probabilistic Systems by Successive Refinements
PAPM-PROBMIV '01 Proceedings of the Joint International Workshop on Process Algebra and Probabilistic Methods, Performance Modeling and Verification
Simple on-the-fly automatic verification of linear temporal logic
Proceedings of the Fifteenth IFIP WG6.1 International Symposium on Protocol Specification, Testing and Verification XV
Experiments with deterministic ω-automata for formulas of linear temporal logic
Theoretical Computer Science - Implementation and application of automata
On the Complexity of Numerical Analysis
SIAM Journal on Computing
Model-checking ω-regular properties of interval Markov chains
FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
Decision problems for interval Markov chains
LATA'11 Proceedings of the 5th international conference on Language and automata theory and applications
Formal verification and simulation for performance analysis for probabilistic broadcast protocols
ADHOC-NOW'06 Proceedings of the 5th international conference on Ad-Hoc, Mobile, and Wireless Networks
Tulip: model checking probabilistic systems using expectation maximisation algorithm
QEST'13 Proceedings of the 10th international conference on Quantitative Evaluation of Systems
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Interval Markov chains (IMCs) generalize ordinary Markov chains by having interval-valued transition probabilities. They are useful for modeling systems in which some transition probabilities depend on an unknown environment, are only approximately known, or are parameters that can be controlled. We consider the problem of computing values for the unknown probabilities in an IMC that maximize the probability of satisfying an ω-regular specification. We give new upper and lower bounds on the complexity of this problem. We then describe an approach based on an expectation maximization algorithm. We provide some analytical guarantees on the algorithm, and show how it can be combined with translation of logic to automata. We give experiments showing that the resulting system gives a practical approach to model checking IMCs.