Algebraic laws for nondeterminism and concurrency
Journal of the ACM (JACM)
Three partition refinement algorithms
SIAM Journal on Computing
Characterizing finite Kripke structures in propositional temporal logic
Theoretical Computer Science - International Joint Conference on Theory and Practice of Software Development, P
Three logics for branching bisimulation
Journal of the ACM (JACM)
Model checking
Making abstract interpretations complete
Journal of the ACM (JACM)
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Systematic design of program analysis frameworks
POPL '79 Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Data Structures and Algorithms
Data Structures and Algorithms
An Efficient Algorithm for Branching Bisimulation and Stuttering Equivalence
ICALP '90 Proceedings of the 17th International Colloquium on Automata, Languages and Programming
Why Is Simulation Harder than Bisimulation?
CONCUR '02 Proceedings of the 13th International Conference on Concurrency Theory
Incompleteness, Counterexamples, and Refinements in Abstract Model-Checking
SAS '01 Proceedings of the 8th International Symposium on Static Analysis
Computing simulations on finite and infinite graphs
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
From Bisimulation to Simulation: Coarsest Partition Problems
Journal of Automated Reasoning
Imcompleteness of States w.r.t traces in model Checking
Information and Computation
A calculus of logical relations for over- and underapproximating static analyses
Science of Computer Programming
What You Lose is What You Leak: Information Leakage in Declassification Policies
Electronic Notes in Theoretical Computer Science (ENTCS)
Generalizing the Paige--Tarjan algorithm by abstract interpretation
Information and Computation
Incompleteness of states w.r.t. traces in model checking
Information and Computation
Deriving bisimulations by simplifying partitions
VMCAI'08 Proceedings of the 9th international conference on Verification, model checking, and abstract interpretation
A forward-backward abstraction refinement algorithm
VMCAI'08 Proceedings of the 9th international conference on Verification, model checking, and abstract interpretation
Underapproximating predicate transformers
SAS'06 Proceedings of the 13th international conference on Static Analysis
An abstract interpretation perspective on linear vs. branching time
APLAS'05 Proceedings of the Third Asian conference on Programming Languages and Systems
Modelling declassification policies using abstract domain completeness
Mathematical Structures in Computer Science - Programming Language Interference and Dependence
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
Comparing completeness properties of static analyses and their logics
APLAS'06 Proceedings of the 4th Asian conference on Programming Languages and Systems
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The Paige and Tarjan algorithm (PT) for computing the coarsest refinement of a state partition which is a bisimulation on some Kripke structure is well known. It is also well known in abstract model checking that bisimulation is equivalent to strong preservation of CTL and in particular of Hennessy-Milner logic. Building on these facts, we analyze the basic steps of the PT algorithm from an abstract interpretation perspective, which allows us to reason on strong preservation in the context of generic inductively defined (temporal) languages and of abstract models specified by abstract interpretation. This leads us to design a generalized Paige-Tarjan algorithm, called GPT, for computing the minimal refinement of an abstract interpretation-based model that strongly preserves some given language. It turns out that PT can be obtained by instantiating GPT to the domain of state partitions for the case of strong preservation of Hennessy-Milner logic. We provide a number of examples showing that GPT is of general use. We show how two well-known efficient algorithms for computing simulation and stuttering equivalence can be viewed as simple instances of GPT. Moreover, we instantiate GPT in order to design a O(|Transitions||States|)-time algorithm for computing the coarsest refinement of a given partition that strongly preserves the language generated by the reachability operator EF.