Randomized algorithms
An abstract Monte-Carlo method for the analysis of probabilistic programs
POPL '01 Proceedings of the 28th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Understanding Molecular Simulation
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Abstraction, Refinement And Proof For Probabilistic Systems (Monographs in Computer Science)
Abstraction, Refinement And Proof For Probabilistic Systems (Monographs in Computer Science)
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Abstract interpretation of programs as Markov decision processes
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CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
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IEEE Transactions on Knowledge and Data Engineering
HVC '08 Proceedings of the 4th International Haifa Verification Conference on Hardware and Software: Verification and Testing
Computational Complexity: A Modern Approach
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CMSB '09 Proceedings of the 7th International Conference on Computational Methods in Systems Biology
IBAL: a probabilistic rational programming language
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
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TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
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SAS'10 Proceedings of the 17th international conference on Static analysis
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FORMATS'10 Proceedings of the 8th international conference on Formal modeling and analysis of timed systems
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CAV'11 Proceedings of the 23rd international conference on Computer aided verification
PRISM 4.0: verification of probabilistic real-time systems
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
Probabilistically accurate program transformations
SAS'11 Proceedings of the 18th international conference on Static analysis
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CSF '11 Proceedings of the 2011 IEEE 24th Computer Security Foundations Symposium
A generalization of p-boxes to affine arithmetic
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Probabilistic abstract interpretation
ESOP'12 Proceedings of the 21st European conference on Programming Languages and Systems
Probabilistic symbolic execution
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Green: reducing, reusing and recycling constraints in program analysis
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Reliability analysis in symbolic pathfinder
Proceedings of the 2013 International Conference on Software Engineering
Bayesian inference using data flow analysis
Proceedings of the 2013 9th Joint Meeting on Foundations of Software Engineering
On-the-fly detection of instability problems in floating-point program execution
Proceedings of the 2013 ACM SIGPLAN international conference on Object oriented programming systems languages & applications
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Proceedings of the 2013 ACM SIGPLAN international conference on Object oriented programming systems languages & applications
Uncertain: a first-order type for uncertain data
Proceedings of the 19th international conference on Architectural support for programming languages and operating systems
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We propose an approach for the static analysis of probabilistic programs that sense, manipulate, and control based on uncertain data. Examples include programs used in risk analysis, medical decision making and cyber-physical systems. Correctness properties of such programs take the form of queries that seek the probabilities of assertions over program variables. We present a static analysis approach that provides guaranteed interval bounds on the values (assertion probabilities) of such queries. First, we observe that for probabilistic programs, it is possible to conclude facts about the behavior of the entire program by choosing a finite, adequate set of its paths. We provide strategies for choosing such a set of paths and verifying its adequacy. The queries are evaluated over each path by a combination of symbolic execution and probabilistic volume-bound computations. Each path yields interval bounds that can be summed up with a "coverage" bound to yield an interval that encloses the probability of assertion for the program as a whole. We demonstrate promising results on a suite of benchmarks from many different sources including robotic manipulators and medical decision making programs.