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arXiv · 2206.06866

EXPTIME-hardness of higher-dimensional Minkowski spacetime

Robin Hirsch·Brett McLean
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Abstract

We prove the EXPTIME-hardness of the validity problem for the basic temporal logic on Minkowski spacetime with more than one space dimension. We prove this result for both the lightspeed-or-slower and the slower-than-light accessibility relations (and for both the irreflexive and the reflexive versions of these relations). As an auxiliary result, we prove the EXPTIME-hardness of validity on any frame for which there exists an embedding of the infinite complete binary tree satisfying certain conditions. The proof is by a reduction from the two-player corridor-tiling game.

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Robin Hirsch, Brett McLean. 2022-06-14. EXPTIME-hardness of higher-dimensional Minkowski spacetime. https://arxiv.org/abs/2206.06866

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