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arXiv · 2204.12253

The Pseudo-Reachability Problem for Diagonalisable Linear Dynamical Systems

Julian D'Costa·Toghrul Karimov·Rupak Majumdar·Joël Ouaknine·Mahmoud Salamati·James Worrell
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Abstract

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.

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Julian D'Costa, Toghrul Karimov, Rupak Majumdar, Joël Ouaknine, Mahmoud Salamati, James Worrell. 2022-04-26. The Pseudo-Reachability Problem for Diagonalisable Linear Dynamical Systems. https://arxiv.org/abs/2204.12253

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