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We propose a formal proof of the undecidability of the model checking problemfor alternating- time temporal logic under imperfect information and perfectrecall semantics. This problem was announced to be undecidable according to apersonal communication on multi-player games with imperfect information, but noformal proof was ever published. Our proof is based on a direct reduction fromthe non-halting problem for Turing machines.

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