According to the Codex there is a build in way to allow Authors to edit their own published posts:
◾ Since 2.0
◾ User can edit their published posts. This capability is off by default.
◾ The core checks the capability edit_posts, but on demand this check is changed to edit_published_posts.
However I did not find where I could change this. Is it in a php file? Do I add a filter to functions.php? Is it set in Mysql?
I really would like to avoid using another plugin.