Abstract debugging of higher-order imperative languages
PLDI '93 Proceedings of the ACM SIGPLAN 1993 conference on Programming language design and implementation
Generating data flow analysis algorithms from modal specifications
TACS'91 Selected papers of the conference on Theoretical aspects of computer software
Model checking and abstraction
ACM Transactions on Programming Languages and Systems (TOPLAS)
Property preserving abstractions for the verification of concurrent systems
Formal Methods in System Design - Special issue on computer-aided verification (based on CAV'92 workshop)
Abstract interpretation of reactive systems
ACM Transactions on Programming Languages and Systems (TOPLAS)
Data flow analysis is model checking of abstract interpretations
POPL '98 Proceedings of the 25th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
The reduced relative power operation on abstract domains
Theoretical Computer Science
Temporal abstract interpretation
Proceedings of the 27th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Making abstract interpretations complete
Journal of the ACM (JACM)
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Parametric shape analysis via 3-valued logic
ACM Transactions on Programming Languages and Systems (TOPLAS)
Systematic design of program analysis frameworks
POPL '79 Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Combining Forward and Backward Analyses of Temporal Properties
PADO '01 Proceedings of the Second Symposium on Programs as Data Objects
Property Checking Driven Abstract Interpretation-Based Static Analysis
VMCAI 2003 Proceedings of the 4th International Conference on Verification, Model Checking, and Abstract Interpretation
CONCUR '95 Proceedings of the 6th International Conference on Concurrency Theory
Optimality in Abstractions of Model Checking
SAS '95 Proceedings of the Second International Symposium on Static Analysis
Incompleteness, Counterexamples, and Refinements in Abstract Model-Checking
SAS '01 Proceedings of the 8th International Symposium on Static Analysis
Proof System for Hennessy-Milner Logic with Recursion
CAAP '88 Proceedings of the 13th Colloquium on Trees in Algebra and Programming
The Existence of Finite Abstractions for Branching Time Model Checking
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
3-Valued Abstraction: More Precision at Less Cost
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
A calculus of logical relations for over- and underapproximating static analyses
Science of Computer Programming
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
An abstract interpretation-based refinement algorithm for strong preservation
TACAS'05 Proceedings of the 11th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Strong preservation of temporal fixpoint-based operators by abstract interpretation
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
Extracting Program Logics From Abstract Interpretations Defined by Logical Relations
Electronic Notes in Theoretical Computer Science (ENTCS)
Abstract Interpretation from a Topological Perspective
SAS '09 Proceedings of the 16th International Symposium on Static Analysis
Internal and external logics of abstract interpretations
VMCAI'08 Proceedings of the 9th international conference on Verification, model checking, and abstract interpretation
Comparing completeness properties of static analyses and their logics
APLAS'06 Proceedings of the 4th Asian conference on Programming Languages and Systems
Inverse-limit and topological aspects of abstract interpretation
Theoretical Computer Science
Under-approximations of computations in real numbers based on generalized affine arithmetic
SAS'07 Proceedings of the 14th international conference on Static Analysis
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We study the underapproximation of the predicate transformers used to give semantics to the modalities in dynamic and temporal logic. Because predicate transformers operate on state sets, we define appropriate powerdomains for sound approximation. We study four such domains — two are based on “set inclusion” approximation, and two are based on “quantification” approximation — and we apply the domains to synthesize the most precise, underapproximating $\widetilde{pre}$ and pre transformers, in the latter case, introducing a focus operation. We also show why the expected abstractions of post and $\widetilde{post}$ are unsound, and we use the powerdomains to guide us to correct, sound underapproximations.