On the Complexity of the Escape Problem for Linear Dynamical Systems over Compact Semialgebraic Sets

Julian D'Costa; Engel Lefaucheux; Eike Neumann; Joël Ouaknine; James Worrell

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arXiv · 2107.02060

On the Complexity of the Escape Problem for Linear Dynamical Systems over Compact Semialgebraic Sets

Julian D'Costa·Engel Lefaucheux·Eike Neumann·Joël Ouaknine·James Worrell

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Abstract

We study the computational complexity of the Escape Problem for discrete-time linear dynamical systems over compact semialgebraic sets, or equivalently the Termination Problem for affine loops with compact semialgebraic guard sets. Consider the fragment of the theory of the reals consisting of negation-free $\exists \forall$-sentences without strict inequalities. We derive several equivalent characterisations of the associated complexity class which demonstrate its robustness and illustrate its expressive power. We show that the Compact Escape Problem is complete for this class.

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Julian D'Costa, Engel Lefaucheux, Eike Neumann, Joël Ouaknine, James Worrell. 2021-07-05. On the Complexity of the Escape Problem for Linear Dynamical Systems over Compact Semialgebraic Sets. https://arxiv.org/abs/2107.02060

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