Abstract
This paper proposes a new approach, grounded in Satisfiability Modulo Theories (SMT), to study the transient of a Max-Plus Linear (MPL) system, that is the number of steps leading to its periodic regime. Differently from state-of-the-art techniques, our approach allows the analysis of periodic behaviors for subsets of initial states, as well as the characterization of sets of initial states exhibiting the same specific periodic behavior and transient. Our experiments show that the proposed technique dramatically outperforms state-of-the-art methods based on max-plus algebra computations for systems of large dimensions.
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Notes
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- 2.
Because we regard \(\mathbb {R}^n\) to be the state space of the MPL system (2), we only consider eigenvectors with finite elements.
- 3.
In this reference, one can find the cyclicity for reducible and irreducible matrices using graph-theoretical approaches.
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Abate, A., Cimatti, A., Micheli, A., Mufid, M.S. (2020). Computation of the Transient in Max-Plus Linear Systems via SMT-Solving. In: Bertrand, N., Jansen, N. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2020. Lecture Notes in Computer Science(), vol 12288. Springer, Cham. https://doi.org/10.1007/978-3-030-57628-8_10
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