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arXiv 2104.08980cs.LOcs.FL
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用于LTL验证的采样多项式轨迹

Sampling Polynomial Trajectories for LTL Verification

Daniel Selvaratnam, Michael Cantoni, J. M. Davoren, Iman Shames

摘要:

本文研究了线性时序逻辑规范(LTL without 'next')下连续时间多项式样条轨迹的验证问题。每个原子命题被假定为表示由多元多项式不等式描述的状态空间区域。所提出的方法采样的轨迹战略,以捕捉每一个区域的过渡。这就产生了一个离散的词,称为跟踪,它服从于已建立的路径检查的形式化方法。原连续时间轨迹满足规范,当且仅当其迹。一般的拓扑条件的样本点的推导,确保记录的轨迹为任意连续的路径,任意区域的描述。利用计算机代数的技术,当路径和区域边界由多项式定义时,开发了一种轨迹生成算法来满足这些条件。提出的PolyTrace算法具有多项式复杂性的原子命题的数量,并保证产生的任何多项式路径的轨迹。其性能通过数值例子和机器人的案例研究证明。

英文摘要:

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 samples a trajectory strategically, to capture every one of its region transitions. This yields a discrete word called a trace, which is amenable to established formal methods for path checking. The original continuous-time trajectory is shown to satisfy the specification if and only if its 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 examples and a case study from robotics.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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