The temporal logic of reactive and concurrent systems
The temporal logic of reactive and concurrent systems
Over words, two variables are as powerful as one quantifier alternation
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Simple on-the-fly automatic verification of linear temporal logic
Proceedings of the Fifteenth IFIP WG6.1 International Symposium on Protocol Specification, Testing and Verification XV
Checking Safety Properties Using Induction and a SAT-Solver
FMCAD '00 Proceedings of the Third International Conference on Formal Methods in Computer-Aided Design
Symbolic Model Checking without BDDs
TACAS '99 Proceedings of the 5th International Conference on Tools and Algorithms for Construction and Analysis of Systems
Property Checking via Structural Analysis
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Applying SAT Methods in Unbounded Symbolic Model Checking
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Efficient SAT-based unbounded symbolic model checking using circuit cofactoring
Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
Model checking: algorithmic verification and debugging
Communications of the ACM - Scratch Programming for All
On the Magnitude of Completeness Thresholds in Bounded Model Checking
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
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Bounded model checking is a symbolic bug-finding method that examines paths of bounded length for violations of a given LTL formula. Its rapid adoption in industry owes much to advances in SAT technology over the past 10-15 years. More recently, there have been increasing efforts to apply SAT-based methods to unbounded model checking. One such approach is based on computing a completeness threshold: a bound k such that, if no counterexample of length k or less to a given LTL formula is found, then the formula in fact holds over all infinite paths in the model. The key challenge lies in determining sufficiently small completeness thresholds. In this paper, we show that if the Büchi automaton associated with an LTL formula is cliquey, i.e., can be decomposed into clique-shaped strongly connected components, then the associated completeness threshold is linear in the recurrence diameter of the Kripke model under consideration. We moreover establish that all unary temporal logic formulas give rise to cliquey automata, and observe that this group includes a vast range of specifications used in practice, considerably strengthening earlier results, which report manageable thresholds only for elementary formulas of the form F p and G q.