Some algebraic and geometric computations in PSPACE
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
The complexity of probabilistic verification
Journal of the ACM (JACM)
Measures of uncertainty in expert systems
Artificial Intelligence
Modeling and verification of randomized distributed real-time systems
Modeling and verification of randomized distributed real-time systems
Languages, automata, and logic
Handbook of formal languages, vol. 3
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Introduction to Algorithms
Model Checking of Probabalistic and Nondeterministic Systems
Proceedings of the 15th Conference on Foundations of Software Technology and Theoretical Computer Science
Quantitative stochastic parity games
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
QEST '04 Proceedings of the The Quantitative Evaluation of Systems, First International Conference
Automatic verification of probabilistic concurrent finite state programs
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Model-Checking markov chains in the presence of uncertainties
TACAS'06 Proceedings of the 12th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Don’t know in probabilistic systems
SPIN'06 Proceedings of the 13th international conference on Model Checking Software
Probabilistic Logical Characterization
Information and Computation
New results for Constraint Markov Chains
Performance Evaluation
On the complexity of model checking interval-valued discrete time Markov chains
Information Processing Letters
LTL model checking of interval markov chains
TACAS'13 Proceedings of the 19th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Polynomial-Time verification of PCTL properties of MDPs with convex uncertainties
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
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We study the problem of model checking Interval-valued Discrete-time Markov Chains (IDTMC). IDTMCs are discrete-time finite Markov Chains for which the exact transition probabilities are not known. Instead in IDTMCs, each transition is associated with an interval in which the actual transition probability must lie.We consider two semantic interpretations for the uncertainty in the transition probabilities of an IDTMC. In the first interpretation, we think of an IDTMC as representing a (possibly uncountable) family of (classical) discrete-time Markov Chains, where each member of the family is a Markov Chain whose transition probabilities lie within the interval range given in the IDTMC.We call this semantic interpretation Uncertain Markov Chains (UMC). In the second semantics for an IDTMC, which we call Interval Markov Decision Process (IMDP), we view the uncertainty as being resolved through non-determinism. In other words, each time a state is visited, we adversarially pick a transition distribution that respects the interval constraints, and take a probabilistic step according to the chosen distribution. We introduce a logic ω-PCTL that can express liveness, strong fairness, and ω-regular properties (such properties cannot be expressed in PCTL). We show that the ω-PCTL model checking problem for Uncertain Markov Chain semantics is decidable in PSPACE (same as the best known upper bound for PCTL) and for Interval Markov Decision Process semantics is decidable in coNP (improving the previous known PSPACE bound for PCTL).We also show that the qualitative fragment of the logic can be solved in coNP for the UMC interpretation, and can be solved in polynomial time for a subclass of UMCs.We also prove lower bounds for these model checking problems. We show that the model checking problem of IDTMCs with LTL formulas can be solved for both UMC and IMDP semantics by reduction to the model checking problem of IDTMC with ω-PCTL formulas.