Year: 2025
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Gerlach, Lina, Löding, Christof, Ábrahám, Erika
Institution: RWTH Aachen University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4417539285
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