Model-checking continuous-time Markov chains
ACM Transactions on Computational Logic (TOCL)
Concurrent constraint programming: towards probabilistic abstract interpretation
Proceedings of the 2nd ACM SIGPLAN international conference on Principles and practice of declarative programming
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
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
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
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
Abstract Interpretation of Probabilistic Semantics
SAS '00 Proceedings of the 7th International Symposium on Static Analysis
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CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Abstraction, Refinement And Proof For Probabilistic Systems (Monographs in Computer Science)
Abstraction, Refinement And Proof For Probabilistic Systems (Monographs in Computer Science)
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Science of Computer Programming - Special issue: Static analysis symposium (SAS 2003)
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Theoretical Computer Science - Quantitative aspects of programming languages (QAPL 2004)
Game-based Abstraction for Markov Decision Processes
QEST '06 Proceedings of the 3rd international conference on the Quantitative Evaluation of Systems
Probabilistic Model Checking Modulo Theories
QEST '07 Proceedings of the Fourth International Conference on Quantitative Evaluation of Systems
Least Upper Bounds for Probability Measures and Their Applications to Abstractions
CONCUR '08 Proceedings of the 19th international conference on Concurrency Theory
Comparative branching-time semantics for Markov chains
Information and Computation
Three-valued abstraction for continuous-time Markov chains
CAV'07 Proceedings of the 19th international conference on Computer aided verification
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CAV'11 Proceedings of the 23rd international conference on Computer aided verification
Probability and nondeterminism in operational models of concurrency
CONCUR'06 Proceedings of the 17th international conference on Concurrency Theory
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
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Least upper bounds play an important role in defining the semantics of programming languages, and in abstract interpretations. In this paper, we identify conditions on countable ordered measurable spaces that ensure the existence of least upper bounds for all sets of probability measures. These conditions are shown to be necessary as well - for any measurable space not satisfying these conditions, there are (finite) sets of probability measures for which no least upper bound exists. For measurable spaces meeting these conditions, the existence of least upper bounds is established constructively. Based on this least upper bound construction, we present a novel abstraction method applicable to Discrete Time Markov Chains (DTMCs), Markov Decision Processes (MDPs), and Continuous Time Markov Chains (CTMCs). The main advantage of the new abstraction techniques is that the resulting abstract models are purely probabilistic that may be more amenable to automated analysis than models with both nondeterministic and probabilistic transitions which arise from previously known abstraction techniques.