The complexity of stochastic games
Information and Computation
Concurrent constraint programming: towards probabilistic abstract interpretation
Proceedings of the 2nd ACM SIGPLAN international conference on Principles and practice of declarative programming
Systematic design of program transformation frameworks by abstract interpretation
POPL '02 Proceedings of the 29th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Principles of Program Analysis
Principles of Program Analysis
Backwards Abstract Interpretation of Probabilistic Programs
ESOP '01 Proceedings of the 10th European Symposium on Programming Languages and Systems
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
Model Checking of Probabalistic and Nondeterministic Systems
Proceedings of the 15th Conference on Foundations of Software Technology and Theoretical Computer Science
Boolean and Cartesian Abstraction for Model Checking C Programs
TACAS 2001 Proceedings of the 7th International Conference on Tools and Algorithms for the Construction and Analysis of Systems
Cache Behavior Prediction by Abstract Interpretation
SAS '96 Proceedings of the Third International Symposium on Static Analysis
On probabilistic program equivalence and refinement
CONCUR 2005 - Concurrency Theory
Abstract interpretation of programs as Markov decision processes
Science of Computer Programming - Special issue: Static analysis symposium (SAS 2003)
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
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Game-Based Probabilistic Predicate Abstraction in PRISM
Electronic Notes in Theoretical Computer Science (ENTCS)
Probabilistic Abstract Interpretation of Imperative Programs using Truncated Normal Distributions
Electronic Notes in Theoretical Computer Science (ENTCS)
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)
On automated verification of probabilistic programs
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
ESOP'05 Proceedings of the 14th European conference on Programming Languages and Systems
PRISM: a tool for automatic verification of probabilistic systems
TACAS'06 Proceedings of the 12th international conference on Tools and Algorithms for the Construction and Analysis of Systems
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
Probabilistic abstractions with arbitrary domains
SAS'11 Proceedings of the 18th international conference on Static analysis
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
Heuristics for probabilistic timed automata with abstraction refinement
MMB'12/DFT'12 Proceedings of the 16th international GI/ITG conference on Measurement, Modelling, and Evaluation of Computing Systems and Dependability and Fault Tolerance
Probabilistic abstract interpretation
ESOP'12 Proceedings of the 21st European conference on Programming Languages and Systems
Variable probabilistic abstraction refinement
ATVA'12 Proceedings of the 10th international conference on Automated Technology for Verification and Analysis
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This paper investigates relative precision and optimality of analyses for concurrent probabilistic systems. Aiming at the problem at the heart of probabilistic model checking – computing the probability of reaching a particular set of states – we leverage the theory of abstract interpretation. With a focus on predicate abstraction, we develop the first abstract-interpretation framework for Markov decision processes which admits to compute both lower and upper bounds on reachability probabilities. Further, we describe how to compute and approximate such abstractions using abstraction refinement and give experimental results.