Abstract interpretation and application to logic programs
Journal of Logic Programming
Abstract interpretation: a semantics-based tool for program analysis
Handbook of logic in computer science (vol. 4)
Abstract interpretation of reactive systems
ACM Transactions on Programming Languages and Systems (TOPLAS)
The quotient of an abstract interpretation
Theoretical Computer Science
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
Principles of Program Analysis
Principles of Program Analysis
Systematic design of program analysis frameworks
POPL '79 Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Probabilistic Concurrent Constraint Programming: Towards a Fully Abstract Model
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
Completeness in Abstract Interpretation: A Domain Perspective
AMAST '97 Proceedings of the 6th International Conference on Algebraic Methodology and Software Technology
An Operational Semantics for Probabilistic Concurrent Constraint Programming
ICCL '98 Proceedings of the 1998 International Conference on Computer 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
Analysing Approximate Confinement under Uniform Attacks
SAS '02 Proceedings of the 9th International Symposium on Static Analysis
Probabilistic semantics and program analysis
SFM'10 Proceedings of the Formal methods for quantitative aspects of programming languages, and 10th international conference on School on formal methods for the design of computer, communication and software systems
Linear-invariant generation for probabilistic programs: automated support for proof-based methods
SAS'10 Proceedings of the 17th international conference on Static analysis
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We develop a methodology for constructing semantics-based analyses of programs by approximating their probabilistic semantics. The framework we introduce resembles the one based on Galois connections used in abstract interpretation, the main difference being the choice of linear space structures instead of order-theoretic ones as semantical (concrete and abstract) domains. The intrinsic quantitative nature of linear spaces makes the method suitable for investigations on the problem of a numerical comparison of abstract interpretations with respect to their precision. After introducing the notion of probabilistic abstract interpretation, we define a measure of its precision by means of the norm of a linear operator which encodes the "incompleteness" of the abstraction. Finally we show the application of our results in a series of classical examples.