This work discusses the reachability analysis (RA) of Max-Plus Linear (MPL) systems, a class of continuous-space, discrete-event models defined over the max-plus algebra. Given the initial and target sets, we develop algorithms to verify whether there exist trajectories of the MPL system that, starting from the initial set, eventually reach the target set. We show that RA can be solved symbolically by encoding the MPL system, as well as initial and target sets into difference logic, and then checking the satisfaction of the resulting logical formula via an off-the-shelf satisfiability modulo theories (SMT) solver. The performance and scalability of the developed SMT-based algorithms are shown to clearly outperform state-of-the-art RA algorithms for MPL systems, newly allowing to investigate RA of high-dimensional MPL systems: the verification of models with more than 100 continuous variables shows the applicability of these techniques to MPL systems of industrial relevance.

中文翻译：

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高维 Max-Plus 线性系统的符号可达性分析

这项工作讨论了最大加线性 (MPL) 系统的可达性分析 ​​(RA)，这是一类在最大加代数上定义的连续空间离散事件模型。给定初始集和目标集，我们开发算法来验证 MPL 系统是否存在从初始集开始最终到达目标集的轨迹。我们表明，可以通过将 MPL 系统以及初始和目标集编码为差分逻辑，然后通过现成的可满足性模理论 (SMT) 求解器检查所得逻辑公式的满意度来象征性地求解 RA。所开发的基于 SMT 的算法的性能和可扩展性明显优于 MPL 系统的最先进的 RA 算法，新允许研究高维 MPL 系统的 RA：