Model-checking ATL under Imperfect Information and Perfect Recall Semantics is Undecidable

We propose a formal proof of the undecidability of the model checking problem for alternatingtime temporal logic under imperfect information and perfect recall semantics. This problem was announced to be undecidable according to a personal communication on multi-player games with imperfect information, but no formal proof was ever published. Our proof is based on a direct reduction from the non-halting problem for Turing machines.

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