The temporal logic of reactive and concurrent systems
The temporal logic of reactive and concurrent systems
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)
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
Systematic design of program analysis frameworks
POPL '79 Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Counterexample-Guided Abstraction Refinement
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
On Small Depth Threshold Circuits
SWAT '92 Proceedings of the Third Scandinavian Workshop on Algorithm Theory
Making Abstract Model Checking Strongly Preserving
SAS '02 Proceedings of the 9th International Symposium on Static Analysis
Incompleteness, Counterexamples, and Refinements in Abstract Model-Checking
SAS '01 Proceedings of the 8th International Symposium on Static Analysis
States vs. Traces in Model Checking by Abstract Interpretation
SAS '02 Proceedings of the 9th International Symposium 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
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In POPL'00, Cousot and Cousot introduced and studied a novel general temporal specification language, called µ-calculus, in particular featuring a natural and rich time-symmetric trace-based semantics. The classical state-based model checking of the µ-calculus is an abstract interpretation of its trace-based semantics, which, surprisingly, turns out to be incomplete, even for finite systems. Cousot and Cousot identified the temporal connectives causing such incompleteness. In this paper, we first characterize the least, i.e. least informative, refinements of the state-based model checking abstraction which are complete relatively to any incomplete temporal connective. On the basis of this analysis, we show that the least refinement of the state-based model checking semantics of (a slight and natural monotone restriction of) the µ-calculus which is complete w.r.t. the trace-based semantics does exist, and it is essentially the trace-based semantics itself. This result can be read as stating that any model checking algorithm for the µ-calculus abstracting away from sets of traces will be necessarily incomplete.