Algebraic laws for nondeterminism and concurrency
Journal of the ACM (JACM)
Two-level semantics and abstract interpretation
Theoretical Computer Science
Theoretical Computer Science
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: a semantics-based tool for program analysis
Handbook of logic in computer science (vol. 4)
Communication and concurrency
Abstract interpretation of reactive systems
ACM Transactions on Programming Languages and Systems (TOPLAS)
Parametric shape analysis via 3-valued logic
Proceedings of the 26th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A semantics for complex objects and approximate queries
Proceedings of the seventh ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Making abstract interpretations complete
Journal of the ACM (JACM)
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Flow Analysis of Computer Programs
Flow Analysis of Computer Programs
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
ESOP '90 Proceedings of the 3rd European Symposium on Programming
Concurrency and Automata on Infinite Sequences
Proceedings of the 5th GI-Conference on Theoretical Computer Science
A relational framework for abstract interpretation
Programs as Data Objects, Proceedings of a Workshop
Structure-preserving binary relations for program abstraction
The essence of computation
A domain equation for refinement of partial systems
Mathematical Structures in Computer Science
Proof-guided underapproximation-widening for multi-process systems
Proceedings of the 32nd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
The Description Logic Handbook
The Description Logic Handbook
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
Extracting Program Logics From Abstract Interpretations Defined by Logical Relations
Electronic Notes in Theoretical Computer Science (ENTCS)
Sound, complete and scalable path-sensitive analysis
Proceedings of the 2008 ACM SIGPLAN conference on Programming language design and implementation
Loop detection in term rewriting using the eliminating unfoldings
Theoretical Computer Science
Abstract Interpretation from a Topological Perspective
SAS '09 Proceedings of the 16th International Symposium on Static Analysis
Reasoning about the unknown in static analysis
Communications of the ACM
Modal abstractions of concurrent behavior
ACM Transactions on Computational Logic (TOCL)
Underapproximating predicate transformers
SAS'06 Proceedings of the 13th international conference on Static Analysis
Fluid updates: beyond strong vs. weak updates
ESOP'10 Proceedings of the 19th European conference on Programming Languages and Systems
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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Motivated by Dennis Dams' studies of over- and underapproximation of state-transition systems, we define a logical-relation calculus for Galois-connection building. The calculus lets us define overapproximating Galois connections in terms of lower powersets and underapproximating Galois connections in terms of upper powersets. Using the calculus, we synthesize Dams' most-precise over- and underapproximating transition systems and obtain proofs of their soundness and best precision as corollaries of abstract-interpretation theory. As a bonus, the calculus yields a logic that corresponds to the variant of Hennessy-Milner logic used in Dams' results. Following from a corollary, we have that Dams' most-precise approximations soundly validate most properties that hold true for the corresponding concrete system. These results bind together abstract interpretation and abstract model checking, as intended by Dams.