Competitive Markov decision processes
Competitive Markov decision processes
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
Game-based Abstraction for Markov Decision Processes
QEST '06 Proceedings of the 3rd international conference on the Quantitative Evaluation of Systems
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Abstraction Refinement for Probabilistic Software
VMCAI '09 Proceedings of the 10th International Conference on Verification, Model Checking, and Abstract Interpretation
Automated Game Analysis via Probabilistic Model Checking: a case study
Electronic Notes in Theoretical Computer Science (ENTCS)
Magnifying-lens abstraction for Markov decision processes
CAV'07 Proceedings of the 19th international conference on Computer aided verification
A game-based abstraction-refinement framework for Markov decision processes
Formal Methods in System Design
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
PRISM 4.0: verification of probabilistic real-time systems
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
Best probabilistic transformers
VMCAI'10 Proceedings of the 11th international conference on Verification, Model Checking, and Abstract Interpretation
PASS: abstraction refinement for infinite probabilistic models
TACAS'10 Proceedings of the 16th 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
Evaluating the reliability of NAND multiplexing with PRISM
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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Predicate abstraction has proven powerful in the analysis of very large probabilistic systems, but has thus far been limited to the analysis of systems with a fixed number of distinct transition probabilities. This excludes a large variety of potential analysis cases, ranging from sensor networks to biochemical systems. In these systems, transition probabilities are often given as a function of state variables--leading to an arbitrary number of different probabilities. This paper overcomes this shortcoming. It extends existing abstraction techniques to handle such variable probabilities. We first identify the most precise abstraction in this setting, the best transformer. For practicality purposes, we then devise another type of abstraction, mapping on extensions of constraint or interval Markov chains, which is less precise but better applicable in practice. Refinement techniques are employed in case a given abstraction yields too imprecise results. We demonstrate the practical applicability of our method on two case studies.