Model Checking Strategic Abilities of Agents Under Incomplete Information

In this paper we introduce and study the complexity of model checking alternating-time temporal logic (atp) with imperfect information, using a fine-structured complexity measure. While atp model checking with perfect information is linear in the size of the model when the number of agents is considered fixed, this is no longer true when the number of agents is considered parameters of the problem (fine structure). Combining it with results from our previous papers, we get the surprising result that checking strategic abilities of agents under both perfect and imperfect information belong to the same complexity class: both problems are $\sum^P_{2}$-complete.

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