Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
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
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
Linear completeness thresholds for bounded model checking
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
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Bounded model checking (BMC) is a highly successful bug-finding method that examines paths of bounded length for violations of a given regular or omega-regular specification. A completeness threshold for a given model M and specification phi is a bound k such that, if no counterexample to phi of length k or less can be found in M, then M in fact satisfies phi. The quest for 'small' completeness thresholds in BMC goes back to the very inception of the technique, over a decade ago, and remains a topic of active research. For a fixed specification, completeness thresholds are typically expressed in terms of key attributes of the models under consideration, such as their diameter (length of the longest shortest path) and especially their recurrence diameter (length of the longest loop-free path). A recent research paper identified a large class of LTL specifications having completeness thresholds linear in the models' recurrence diameter. However, the authors left open the question of whether linearity is in general even decidable. In the present paper, we settle the problem in the affirmative, by showing that the linearity problem for both regular and omega-regular specifications (provided as automata and Buechi automata respectively is PSPACE-complete. Moreover, we establish the following dichotomies: for regular specifications, completeness thresholds are either linear or exponential, whereas for omega-regular specifications, completeness thresholds are either linear or at least quadratic.