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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.16775 |
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Table of Contents:
- We propose a probabilistic hyperlogic called HyperSt$^2$ that can express hyperproperties of strategies in turn-based stochastic games. To the best of our knowledge, HyperSt$^2$ is the first hyperlogic for stochastic games. HyperSt$^2$ can relate probabilities of several independent executions of strategies in a stochastic game. For example, in HyperSt$^2$ it is natural to formalize optimality, i.e., to express that some strategy is better than all other strategies, or to express the existence of Nash equilibria. We investigate the expressivity of HyperSt$^2$ by comparing it to existing logics for stochastic games, as well as existing hyperlogics. Though the model-checking problem for HyperSt$^2$ is in general undecidable, we show that it becomes decidable for bounded memory and is in EXPTIME and PSPACE-hard over memoryless deterministic strategies, and we identify a fragment for which the model-checking problem is PSPACE-complete.