Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Handbook of theoretical computer science (vol. B): formal models and semantics
Handbook of theoretical computer science (vol. B): formal models and semantics
Handbook of theoretical computer science (vol. B)
Abstract interpretation and application to logic programs
Journal of Logic Programming
Modeling and verification of randomized distributed real-time systems
Modeling and verification of randomized distributed real-time systems
Model checking
An abstract Monte-Carlo method for the analysis of probabilistic programs
POPL '01 Proceedings of the 28th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Quantitative solution of omega-regular games380872
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Reduction and Refinement Strategies for Probabilistic Analysis
PAPM-PROBMIV '02 Proceedings of the Second Joint International Workshop on Process Algebra and Probabilistic Methods, Performance Modeling and Verification
Reduction and Refinement Strategies for Probabilistic Analysis
PAPM-PROBMIV '02 Proceedings of the Second Joint International Workshop on Process Algebra and Probabilistic Methods, Performance Modeling and Verification
Markov Decision Processes and Regular Events (Extended Abstract)
ICALP '90 Proceedings of the 17th International Colloquium on Automata, Languages and Programming
Testing Preorders for Probabilistic Processes
ICALP '92 Proceedings of the 19th International Colloquium on Automata, Languages and Programming
Symbolic Model Checking for Probabilistic Processes
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Abstraction of Expectation Functions Using Gaussian Distributions
VMCAI 2003 Proceedings of the 4th International Conference on Verification, Model Checking, and Abstract Interpretation
Model Checking of Probabalistic and Nondeterministic Systems
Proceedings of the 15th Conference on Foundations of Software Technology and Theoretical Computer Science
Abstract Interpretation of Probabilistic Semantics
SAS '00 Proceedings of the 7th International Symposium on Static Analysis
Efficient dynamic-programming updates in partially observable Markov decision processes
Efficient dynamic-programming updates in partially observable Markov decision processes
A logic for reasoning about time and reability
A logic for reasoning about time and reability
Formal Verification of Probabilistic Systems
Formal Verification of Probabilistic Systems
Least Upper Bounds for Probability Measures and Their Applications to Abstractions
CONCUR '08 Proceedings of the 19th international conference on Concurrency Theory
Abstraction Refinement for Probabilistic Software
VMCAI '09 Proceedings of the 10th International Conference on Verification, Model Checking, and Abstract Interpretation
Approximating Probabilistic Behaviors of Biological Systems Using Abstract Interpretation
Electronic Notes in Theoretical Computer Science (ENTCS)
Probabilistic Model Checking of Biological Systems with Uncertain Kinetic Rates
RP '09 Proceedings of the 3rd International Workshop on Reachability Problems
Bisimulation minimisation mostly speeds up probabilistic model checking
TACAS'07 Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems
Three-valued abstraction for continuous-time Markov chains
CAV'07 Proceedings of the 19th international conference on Computer aided verification
Magnifying-lens abstraction for Markov decision processes
CAV'07 Proceedings of the 19th international conference on Computer aided verification
Abstraction of probabilistic systems
FORMATS'07 Proceedings of the 5th international conference on Formal modeling and analysis of timed systems
A counterexample-guided abstraction-refinement framework for markov decision processes
ACM Transactions on Computational Logic (TOCL)
A game-based abstraction-refinement framework for Markov decision processes
Formal Methods in System Design
Probabilistic model checking of biological systems with uncertain kinetic rates
Theoretical Computer Science
Best probabilistic transformers
VMCAI'10 Proceedings of the 11th international conference on Verification, Model Checking, and Abstract Interpretation
Probabilistic abstract interpretation
ESOP'12 Proceedings of the 21st European conference on Programming Languages and Systems
An analysis for proving probabilistic termination of biological systems
Theoretical Computer Science
Proceedings of the 34th ACM SIGPLAN conference on Programming language design and implementation
Probabilistic program analysis with martingales
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
Least upper bounds for probability measures and their applications to abstractions
Information and Computation
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We propose a formal language for the specification of trace properties of probabilistic, nondeterministic transition systems, encompassing the properties expressible in Linear Time Logic. Those formulas are in general undecidable on infinite deterministic transition systems and thus on infinite Markov decision processes. This language has both a semantics in terms of sets of traces, as well as another semantics in terms of measurable functions; we give and prove theorems linking the two semantics. We then apply abstract interpretation-based techniques to give upper bounds on the worst-case probability of the studied property. We propose an enhancement of this technique when the state space is partitioned -- for instance along the program points -- allowing the use of faster iteration methods.