POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
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
Abstract Interpretation of Probabilistic Semantics
SAS '00 Proceedings of the 7th International Symposium on Static Analysis
Some results on the multivariate truncated normal distribution
Journal of Multivariate Analysis
Quantitative static analysis of distributed systems
Journal of Functional Programming
Abstraction Refinement for Probabilistic Software
VMCAI '09 Proceedings of the 10th International Conference on Verification, Model Checking, and Abstract Interpretation
PLDI '10 Proceedings of the 2010 ACM SIGPLAN conference on Programming language design and implementation
A game-based abstraction-refinement framework for Markov decision processes
Formal Methods in System Design
Probabilistically accurate program transformations
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
Probabilistic abstract interpretation
ESOP'12 Proceedings of the 21st European conference on Programming Languages and Systems
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
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
| Hi-index | 0.00 |
When modelling a complex system, such as one with distributed functionality, we need to choose an appropriate level of abstraction. When analysing quantitative properties of the system, this abstraction is typically probabilistic, since we introduce uncertainty about its state and therefore its behaviour. In particular, when we aggregate several concrete states into a single abstract state we would like to know the distribution over these states. In reality, any probability distribution may be possible, but this leads to an intractable analysis. Therefore, we must find a way to approximate these distributions in a safe manner. We present an abstract interpretation for a simple imperative language with message passing, where truncated multivariate normal distributions are used as the abstraction. This allows the probabilities of transient properties to be bounded, without needing to calculate the exact distribution. We describe the semantics of programs in terms of automata, whose transitions are linear operators on measures. Given an input measure, we generate a probabilistic trace whose states are labelled by measures, describing the distribution of the values of variables at that point. By the use of appropriate widening operators, we are able to abstract the behaviour of loops to various degrees of precision.