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arXiv · 2412.07341

The Complexity of HyperQPTL

Gaëtan Regaud·Martin Zimmermann
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Abstract

HyperQPTL and HyperQPTL$^+$ are expressive specification languages for hyperproperties, properties that relate multiple executions of a system. Tight complexity bounds are known for HyperQPTL finite-state satisfiability and model-checking. Here, we settle the complexity of satisfiability for HyperQPTL as well as satisfiability, finite-state satisfiability, and model-checking for HyperQPTL$^+$: the former is $\Sigma^2_1$-complete, the latter are all equivalent to truth in third-order arithmetic, i.e., all four are very undecidable.

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Gaëtan Regaud, Martin Zimmermann. 2024-12-10. The Complexity of HyperQPTL. https://arxiv.org/abs/2412.07341

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