Abstract
The use of specialised approximations for reachability, instead of exact reachability, has given rise to scalable methods to verify deadlock freedom in the context of distributed finite-state systems. In this work, we extend these approaches to check static properties. These properties capture the immediate/static behaviour of a system. The static nature of these properties make them a good match for the sort of over-approximations we use. Local-deadlock freedom and mutual exclusion are two commonly desired properties for distributed systems that naturally fit into our framework. Local-deadlock freedom, in particular, specifies that no subsystem can reach a permanently blocked state. We show by a series of experiments that our approximate framework can prove such properties for a number of interesting systems, and it can do so more efficiently compared to complete approaches.
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Notes
- 1.
The predicate \(reach_{Pair}\) corresponds to \(pairwise\_reachable\) in [2]. This new name is introduced for uniformity.
- 2.
These predicates correspond to \(reachable^C_{N}\), \(reachable^A_{N}\), \(reachable^C_{S}\), and \(reachable^A_{S}\) in [3], respectively. This renaming is for uniformity.
- 3.
Proofs are given in reports associated to original papers.
- 4.
\(Reach_{Pair}\) corresponds to the formula Reachable in [2] where the pairs in NPR are calculated over sets \(S_i\) and \(S_j\) instead of \(RequireSync_i\) and \(RequireSync_j\). The sets \(RequireSync_i\) represent an optimisation for checking deadlock freedom that is not valid to all static properties. \(Reach_{NC}\), \(Reach_{SC}\), \(Reach_{NA}\) and \(Reach_{SA}\) correspond to formulas \(Reach^C_N\), \(Reach^C_S\), \(Reach^A_N\) and \(Reach^A_S\) in [3], respectively.
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Acknowledgements
The first author is a CAPES Foundation scholarship holder (Process no: 13201/13-1). The other authors are partially sponsored by EPSRC under agreement number EP/N022777.
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Antonino, P., Gibson-Robinson, T., Roscoe, A.W. (2017). Checking Static Properties Using Conservative SAT Approximations for Reachability. In: Cavalheiro, S., Fiadeiro, J. (eds) Formal Methods: Foundations and Applications. SBMF 2017. Lecture Notes in Computer Science(), vol 10623. Springer, Cham. https://doi.org/10.1007/978-3-319-70848-5_15
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