Android & iOS service in Qt
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From what I know, iOS does not support at all "Services". In the recent iOS 7 they improved the background modality for update the app even when is in background. But, it should be a normal app.
So, for iOS the correct question is if it's possible to use the new iOS 7 API to execute code in background. And the answer is Yes, because it's very simple to use objective-C code inside a Qt app.For Android, I don't know which is the difference between an activity and a service. But from what I know, the Qt provides only the android activity.