Bisimulation through probabilistic testing
Information and Computation
An analysis of stochastic shortest path problems
Mathematics of Operations Research
The complexity of stochastic games
Information and Computation
Modeling and verification of randomized distributed real-time systems
Modeling and verification of randomized distributed real-time 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
Computing Minimum and Maximum Reachability Times in Probabilistic Systems
CONCUR '99 Proceedings of the 10th International Conference on Concurrency Theory
Construction of Abstract State Graphs with PVS
CAV '97 Proceedings of the 9th International Conference on Computer Aided Verification
Counterexample-Guided Abstraction Refinement
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
ARTS '99 Proceedings of the 5th International AMAST Workshop on Formal Methods for Real-Time and Probabilistic Systems
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Approximating labelled Markov processes
Information and Computation
QEST '04 Proceedings of the The Quantitative Evaluation of Systems, First International Conference
Model checking for a probabilistic branching time logic with fairness
Distributed Computing
Abstraction, Refinement And Proof For Probabilistic Systems (Monographs in Computer Science)
Abstraction, Refinement And Proof For Probabilistic Systems (Monographs in Computer Science)
Abstract interpretation of programs as Markov decision processes
Science of Computer Programming - Special issue: Static analysis symposium (SAS 2003)
Probabilistic guarded commands mechanized in HOL
Theoretical Computer Science - Quantitative aspects of programming languages (QAPL 2004)
Performance analysis of probabilistic timed automata using digital clocks
Formal Methods in System Design
Game-based Abstraction for Markov Decision Processes
QEST '06 Proceedings of the 3rd international conference on the Quantitative Evaluation of Systems
Theoretical Computer Science
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
Counterexample Generation in Probabilistic Model Checking
IEEE Transactions on Software Engineering
Stochastic Games for Verification of Probabilistic Timed Automata
FORMATS '09 Proceedings of the 7th International Conference on Formal Modeling and Analysis of Timed Systems
Magnifying-lens abstraction for Markov decision processes
CAV'07 Proceedings of the 19th international conference on Computer aided verification
Abstract interpretation for worst and average case analysis
Program analysis and compilation, theory and practice
A counterexample-guided abstraction-refinement framework for markov decision processes
ACM Transactions on Computational Logic (TOCL)
Best probabilistic transformers
VMCAI'10 Proceedings of the 11th international conference on Verification, Model Checking, and Abstract Interpretation
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
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
Don’t know in probabilistic systems
SPIN'06 Proceedings of the 13th international conference on Model Checking Software
PRISM 4.0: verification of probabilistic real-time systems
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
Probabilistic abstractions with arbitrary domains
SAS'11 Proceedings of the 18th international conference on Static analysis
A linear process-algebraic format with data for probabilistic automata
Theoretical Computer Science
Variable probabilistic abstraction refinement
ATVA'12 Proceedings of the 10th international conference on Automated Technology for Verification and Analysis
Compositional abstraction techniques for probabilistic automata
TCS'12 Proceedings of the 7th IFIP TC 1/WG 202 international conference on Theoretical Computer Science
From software verification to `everyware' verification
Computer Science - Research and Development
A property-based abstraction framework for SysML activity diagrams
Knowledge-Based Systems
Model checking for probabilistic timed automata
Formal Methods in System Design
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In the field of model checking, abstraction refinement has proved to be an extremely successful methodology for combating the state-space explosion problem. However, little practical progress has been made in the setting of probabilistic verification. In this paper we present a novel abstraction-refinement framework for Markov decision processes (MDPs), which are widely used for modelling and verifying systems that exhibit both probabilistic and nondeterministic behaviour. Our framework comprises an abstraction approach based on stochastic two-player games, two refinement methods and an efficient algorithm for an abstraction-refinement loop. The key idea behind the abstraction approach is to maintain a separation between nondeterminism present in the original MDP and nondeterminism introduced during the abstraction process, each type being represented by a different player in the game. Crucially, this allows lower and upper bounds to be computed for the values of reachability properties of the MDP. These give a quantitative measure of the quality of the abstraction and form the basis of the corresponding refinement methods. We describe a prototype implementation of our framework and present experimental results demonstrating automatic generation of compact, yet precise, abstractions for a large selection of real-world case studies.