We study fundamental reachability problems on pseudo-orbits of linear dynamical systems. Pseudo-orbits can be viewed as a model of computation with limited precision and pseudo-reachability can be thought of as a robust version of classical reachability. Using an approach based on $o$-minimality of $\reals_{\exp}$ we prove decidability of the discrete-time pseudo-reachability problem with arbitrary semialgebraic targets for diagonalisable linear dynamical systems. We also show that our method can be used to reduce the continuous-time pseudo-reachability problem to the (classical) time-bounded reachability problem, which is known to be conditionally decidable.

翻译：我们研究了线性动态系统伪轨道的基本可达性问题,可将优多轨道视为精确度有限和伪可达性有限的计算模型,可视为典型可达性的一种稳健版本,使用以美元-最小值$===============$为基础的方法,证明离散时间伪可达性问题与可对等线性动态系统任意的半热源性目标的分解性。我们还表明,我们的方法可以用来减少持续时间伪可达性问题,而这种(古典)可达性问题是已知有条件的。