Prophecies all the Way: Game-based Model-Checking for HyperQPTL beyond $\forall^*\exists^*$

Sarah Winter; Martin Zimmermann

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arXiv · 2504.08575

Prophecies all the Way: Game-based Model-Checking for HyperQPTL beyond $\forall^\exists^$

Sarah Winter·Martin Zimmermann

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Abstract

Model-checking HyperLTL, a temporal logic expressing properties of sets of traces with applications to information-flow based security and privacy, has a decidable, but TOWER-complete, model-checking problem. While the classical model-checking algorithm for full HyperLTL is automata-theoretic, more recently, a game-based alternative for the $\forall^*\exists^*$-fragment has been presented. Here, we employ imperfect information-games to extend the game-based approach to full HyperQPTL, which features arbitrary quantifier prefixes and quantification over propositions and can express every $\omega$-regular hyperproperty. As a byproduct of our game-based algorithm, we obtain finite-state implementations of Skolem functions via transducers with lookahead that explain satisfaction or violation of HyperQPTL properties.

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Sarah Winter, Martin Zimmermann. 2025-04-11. Prophecies all the Way: Game-based Model-Checking for HyperQPTL beyond $\forall^*\exists^*$. https://arxiv.org/abs/2504.08575

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