论文标题
您可以逃脱紧凑的多层？
How Fast Can You Escape a Compact Polytope?
论文作者
论文摘要
连续的多层逃逸问题（CPEP）询问凸多层内最初初始化的线性微分方程的每个轨迹最终都可以逃脱多层。我们提供了多项式时间算法来决定紧凑型多面体的CPEP。我们还建立了一个定量均匀的上限，以逃脱给定的多面体所需的时间。此外，我们建立了通过还原为连续情况来终止离散线性循环的迭代范围。
The Continuous Polytope Escape Problem (CPEP) asks whether every trajectory of a linear differential equation initialised within a convex polytope eventually escapes the polytope. We provide a polynomial-time algorithm to decide CPEP for compact polytopes. We also establish a quantitative uniform upper bound on the time required for every trajectory to escape the given polytope. In addition, we establish iteration bounds for termination of discrete linear loops via reduction to the continuous case.
