Abstract
This paper introduces the abstraction of max-plus linear (MPL) systems via predicates. Predicates are automatically selected from system matrix, as well as from the specifications under consideration. We focus on verifying time-difference specifications, which encompass the relation between successive events in MPL systems. We implement a bounded model checking (BMC) procedure over a predicate abstraction of the given MPL system, to verify the satisfaction of time-difference specifications. Our predicate abstractions are experimentally shown to improve on existing MPL abstractions algorithms. Furthermore, with focus on the BMC algorithm, we can provide an explicit upper bound on the completeness threshold by means of the transient and the cyclicity of the underlying MPL system.
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Notes
- 1.
For the sake of simplicity, we write the elements of \(\texttt {fin}_i\) in a strictly increasing order.
- 2.
In this paper, we always use \(p\equiv x_i-x_j\ge c\) as a predicate.
- 3.
Notice that, in Definition 6 we consider \(\mathcal {AP}\) as a set of time-difference propositions.
- 4.
Notice a loop-back transition from \(\hat{s}_k\) to \(\hat{s}_l\) in \(\pi _{loop}\).
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Acknowledgements
The first author is supported by Indonesia Endowment Fund for Education (LPDP), while the third acknowledges the support of the Alan Turing Institute, London, UK.
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Syifa’ul Mufid, M., Adzkiya, D., Abate, A. (2019). Bounded Model Checking of Max-Plus Linear Systems via Predicate Abstractions. In: André, É., Stoelinga, M. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2019. Lecture Notes in Computer Science(), vol 11750. Springer, Cham. https://doi.org/10.1007/978-3-030-29662-9_9
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