“Sometimes” and “not never” revisited: on branching versus linear time temporal logic
Journal of the ACM (JACM) - The MIT Press scientific computation series
Model checking and abstraction
ACM Transactions on Programming Languages and Systems (TOPLAS)
Temporal abstract interpretation
Proceedings of the 27th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
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
"Sometime" is sometimes "not never": on the temporal logic of programs
POPL '80 Proceedings of the 7th ACM SIGPLAN-SIGACT 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
Tree-Like Counterexamples in Model Checking
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
Branching vs. Linear Time: Final Showdown
TACAS 2001 Proceedings of the 7th International Conference on Tools and Algorithms for the Construction and Analysis of Systems
Sometimes and Not Never Re-revisited: On Branching Versus Linear Time
CONCUR '98 Proceedings of the 9th International Conference on Concurrency Theory
States vs. Traces in Model Checking by Abstract Interpretation
SAS '02 Proceedings of the 9th International Symposium on Static Analysis
Relating linear and branching model checking
PROCOMET '98 Proceedings of the IFIP TC2/WG2.2,2.3 International Conference on Programming Concepts and Methods
Counterexample-Guided Abstraction Refinement
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
Expressibility results for linear-time and branching-time logics
Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, School/Workshop
The common fragment of CTL and LTL
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Counterexample-guided abstraction refinement for symbolic model checking
Journal of the ACM (JACM)
An abstract interpretation perspective on linear vs. branching time
APLAS'05 Proceedings of the Third Asian conference on Programming Languages and Systems
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
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Cousot and Cousot introduced and studied a general past/future-time specification language, called μ-calculus, featuring a natural time-symmetric trace-based semantics. The standard state-based semantics of the μ-calculus is an abstract interpretation of its trace-based semantics, which turns out to be incomplete, that is trace-incomplete, even for finite systems. As a consequence, standard state-based model checking of the μ-calculus is incomplete w.r.t, trace-based model checking. This paper shows that any refinement or abstraction of the domain of sets of states induces a corresponding semantics which is still trace-incomplete for any propositional fragment of the μ-calculus. This derives from a number of results, one for each incomplete logical/temporal connective of the μ-calculus, that characterize the structure of models, i.e., transition systems, whose corresponding state-based semantics of the μ-calculus is trace-complete.