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.

中文翻译：

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通过 SMT 求解计算 Max-Plus 线性系统中的瞬态

本文提出了一种基于可满足性模理论 (SMT) 的新方法，用于研究最大加线性 (MPL) 系统的瞬态，即导致其周期性状态的步数。与最先进的技术不同，我们的方法允许分析初始状态子集的周期性行为，以及表现出相同特定周期性行为和瞬态的初始状态集的表征。我们的实验表明，对于大维度系统，所提出的技术显着优于基于最大加代数计算的最新方法。