Probabilistic predicate transformers
ACM Transactions on Programming Languages and Systems (TOPLAS)
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
Constructive design of a hierarchy of semantics of a transition system by abstract interpretation
Theoretical Computer Science
Systematic design of program analysis frameworks
POPL '79 Proceedings of the 6th 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
Probabilistic Abstract Interpretation and Statistical Testing
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
Comparing the Galois Connection and Widening/Narrowing Approaches to Abstract Interpretation
PLILP '92 Proceedings of the 4th International Symposium on Programming Language Implementation and Logic Programming
Abstract Interpretation of Probabilistic Semantics
SAS '00 Proceedings of the 7th International Symposium on Static Analysis
Abstraction, Refinement And Proof For Probabilistic Systems (Monographs in Computer Science)
Abstraction, Refinement And Proof For Probabilistic Systems (Monographs in Computer Science)
Probabilistic λ-calculus and Quantitative Program Analysis
Journal of Logic and Computation
Abstract interpretation of programs as Markov decision processes
Science of Computer Programming - Special issue: Static analysis symposium (SAS 2003)
Using probabilistic model checking in systems biology
ACM SIGMETRICS Performance Evaluation Review
Least Upper Bounds for Probability Measures and Their Applications to Abstractions
CONCUR '08 Proceedings of the 19th international conference on Concurrency Theory
Symbolic Magnifying Lens Abstraction in Markov Decision Processes
QEST '08 Proceedings of the 2008 Fifth International Conference on Quantitative Evaluation of Systems
Probabilistic Abstract Interpretation of Imperative Programs using Truncated Normal Distributions
Electronic Notes in Theoretical Computer Science (ENTCS)
Approximating Probabilistic Behaviors of Biological Systems Using Abstract Interpretation
Electronic Notes in Theoretical Computer Science (ENTCS)
Control Techniques for Complex Networks
Control Techniques for Complex Networks
Formal Methods in System Design
Linear-invariant generation for probabilistic programs: automated support for proof-based methods
SAS'10 Proceedings of the 17th international conference on Static analysis
Formal Aspects of Computing
Best probabilistic transformers
VMCAI'10 Proceedings of the 11th international conference on Verification, Model Checking, and Abstract Interpretation
Proceedings of the 34th ACM SIGPLAN conference on Programming language design and implementation
Verifying quantitative reliability for programs that execute on unreliable hardware
Proceedings of the 2013 ACM SIGPLAN international conference on Object oriented programming systems languages & applications
Probabilistic program analysis with martingales
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
Bridging boolean and quantitative synthesis using smoothed proof search
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
Dynamic enforcement of knowledge-based security policies using probabilistic abstract interpretation
Journal of Computer Security
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Abstract interpretation has been widely used for verifying properties of computer systems. Here, we present a way to extend this framework to the case of probabilistic systems. The probabilistic abstraction framework that we propose allows us to systematically lift any classical analysis or verification method to the probabilistic setting by separating in the program semantics the probabilistic behavior from the (non-)deterministic behavior. This separation provides new insights for designing novel probabilistic static analyses and verification methods. We define the concrete probabilistic semantics and propose different ways to abstract them. We provide examples illustrating the expressiveness and effectiveness of our approach.