The complexity of stochastic games
Information and Computation
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Markov Decision Processes: Discrete Stochastic Dynamic Programming
Markov Decision Processes: Discrete Stochastic Dynamic Programming
Systematic design of program analysis frameworks
POPL '79 Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Abstract Interpretation of Probabilistic Semantics
SAS '00 Proceedings of the 7th International Symposium on Static Analysis
The software model checker Blast: Applications to software engineering
International Journal on Software Tools for Technology Transfer (STTT)
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
Apron: A Library of Numerical Abstract Domains for Static Analysis
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Grids: a domain for analyzing the distribution of numerical values
LOPSTR'06 Proceedings of the 16th international conference on Logic-based program synthesis and transformation
Abstract interpretation of programs as Markov decision processes
SAS'03 Proceedings of the 10th international conference on Static analysis
Automatically refining abstract interpretations
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
A game-based abstraction-refinement framework for Markov decision processes
Formal Methods in System Design
Probabilistic abstractions with arbitrary domains
SAS'11 Proceedings of the 18th international conference on Static analysis
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
Counterexample driven refinement for abstract interpretation
TACAS'06 Proceedings of the 12th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Probabilistic abstractions with arbitrary domains
SAS'11 Proceedings of the 18th international conference on Static analysis
Proving termination of probabilistic programs using patterns
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
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Recent work by Hermanns et al. and Kattenbelt et al. has extended counterexample-guided abstraction refinement (CEGAR) to probabilistic programs. These approaches are limited to predicate abstraction. We present a novel technique, based on the abstract reachability tree recently introduced by Gulavani et al., that can use arbitrary abstract domains and widening operators (in the sense of Abstract Interpretation). We show how suitable widening operators can deduce loop invariants difficult to find for predicate abstraction, and propose refinement techniques.