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)
Science of Computer Programming
A unifying view of abstract domain design
ACM Computing Surveys (CSUR)
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
A Calculus of Communicating Systems
A Calculus of Communicating Systems
Systematic design of program analysis frameworks
POPL '79 Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
ACM Transactions on Computational Logic (TOCL)
An Efficient Algorithm for Branching Bisimulation and Stuttering Equivalence
ICALP '90 Proceedings of the 17th International Colloquium on Automata, Languages and Programming
Refining and Compressing Abstract Domains
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
TACAS 2001 Proceedings of the 7th International Conference on Tools and Algorithms for the Construction and Analysis of Systems
Why Is Simulation Harder than Bisimulation?
CONCUR '02 Proceedings of the 13th International Conference on Concurrency Theory
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
An efficient algorithm for computing bisimulation equivalence
Theoretical Computer Science
A classification of symbolic transition systems
ACM Transactions on Computational Logic (TOCL)
A New Efficient Simulation Equivalence Algorithm
LICS '07 Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science
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
Computing Stuttering Simulations
CONCUR 2009 Proceedings of the 20th International Conference on Concurrency Theory
Fuzzy relation equations and reduction of fuzzy automata
Journal of Computer and System Sciences
Static analysis, abstract interpretation and verification in (constraint logic) programming
A 25-year perspective on logic programming
Bisimulations for fuzzy automata
Fuzzy Sets and Systems
Propositional interpolation and abstract interpretation
ESOP'10 Proceedings of the 19th European conference on Programming Languages and Systems
An Abstract Interpretation framework for genotype elimination algorithms
Theoretical Computer Science
Observational Completeness on Abstract Interpretation
Fundamenta Informaticae - Logic, Language, Information and Computation
Computation of the greatest simulations and bisimulations between fuzzy automata
Fuzzy Sets and Systems
Nondeterministic automata: Equivalence, bisimulations, and uniform relations
Information Sciences: an International Journal
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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 model checking that bisimulation is equivalent to strong preservation of CTL or, equivalently, of Hennessy-Milner logic. Drawing on these observations, 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 arbitrary (temporal) languages and of generic abstract models, possibly different from standard state partitions, 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 is a straight instance of GPT on 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 first show how a well-known efficient algorithm for computing stuttering equivalence can be viewed as a simple instance of GPT. We then instantiate GPT in order to design a new efficient algorithm for computing simulation equivalence that is competitive with the best available algorithms. Finally, we show how GPT allows to deal with strong preservation of new languages by providing an efficient algorithm that computes the coarsest refinement of a given partition that strongly preserves a language generated by the reachability operator.