Say [User A] creates, but does not publish [Node 1]. [Views V] aggregates all of the content type that [Node 1] belongs into. [User B] should not be able to see [Node 1] listed on [Views V], but [User A] should be able to see his own unpublished [Node 1], all through [Views V] which lists out the specific content type.
Currently, if I change the Filter to not filter for Published or Unpublished nodes, then regular members can see the title of unpublished Nodes through the view, despite not having permission to access it (if the user clicks on it, then access denied message is shown). I do not wish for this to occur. However, I can't explicitly filter out unpublished nodes, since I want authors of said nodes to be able to see them (and access/edit them before publishing).
So is it possible to have Views filter out nodes based on the access permission of the current user?
I am using Drupal 7, and Views 3.