The notion of innocent strategy was introduced by Hyland and Ong in order tocapture the interactive behaviour of lambda-terms and PCF programs. An innocentstrategy is defined as an alternating strategy with partial memory, in whichthe strategy plays according to its view. Extending the definition tonon-alternating strategies is problematic, because the traditional definitionof views is based on the hypothesis that Opponent and Proponent alternateduring the interaction. Here, we take advantage of the diagrammaticreformulation of alternating innocence in asynchronous games, in order toprovide a tentative definition of innocence in non-alternating games. The taskis interesting, and far from easy. It requires the combination of trueconcurrency and game semantics in a clean and organic way, clarifying therelationship between asynchronous games and concurrent games in the sense ofAbramsky and Melli\`es. It also requires an interactive reformulation of theusual acyclicity criterion of linear logic, as well as a directed variant, as ascheduling criterion.
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