This paper concerns the verification of continuous-time polynomial spline trajectories against linear temporal logic specifications (LTL without 'next'). Each atomic proposition is assumed to represent a state space region described by a multivariate polynomial inequality. The proposed approach is based on sampling the trajectories in a manner that captures all region transitions, to yield a discrete word called a trace, which is amenable to established formal methods for path checking. The continuous-time trajectory is shown to satisfy the specification if and only if the trace does. General topological conditions on the sample points are derived that ensure a trace is recorded for arbitrary continuous paths, given arbitrary region descriptions. Using techniques from computer algebra, a trace generation algorithm is developed to satisfy these conditions when the path and region boundaries are defined by polynomials. The proposed PolyTrace algorithm has polynomial complexity in the number of atomic propositions, and is guaranteed to produce a trace of any polynomial path. Its performance is demonstrated via numerical simulations.

翻译：本文涉及根据线性时间逻辑规格( LTL 不含“ 下一步” ) 校验连续时间多角度的多角度样条轨迹。 假设每个原子主张代表多变量多元性不平等所描述的状态空间区域。 提议的方法基于对轨迹进行取样, 捕捉所有区域的过渡, 产生一个叫“ 痕量” 的单词, 以产生一个叫做“ 痕量” 的单词, 这符合既定的正规路径检查方法。 连续时间轨迹显示在轨迹发生时才符合规格。 样点的一般地貌条件是, 以确保任意连续路径的踪迹记录, 并给出任意区域描述。 使用计算机代数技术, 开发一种痕量生成算法, 以满足这些路径和区域边界由多数值界定的情况。 拟议的多角度图谱算法在原子主张的数量上具有多层次的复杂性, 并且保证产生任何多层次路径的痕迹。 它的性表现通过数字模拟得到证明。