Should we create a tag heap-automata in this case? As far as I know, the concept is novel so there is no common association; the tag would only be used to string these questions together.
As long as Patrick87 links the questions together, which he has, I think this is sufficient. Unless/until heap automata become a revolutionary new concept, it's a good idea to keep the tags as general as possible, so no [heap-automata] tag. Tags such as series etc do not make sense in isolation, outside of the specific question, so I don't see how they will be useful.
Since the concept of heap automata isn't really canonical, I'd be wary of introducing one just for this example. I mean, that seems even more problematic than adding a separate tag for each algorithm or data structure.
Perhaps what would be more appropriate would be a series, series-of-questions, or follow-up tag, for the more general case of somebody asking a question, getting an answer, and asking a closely-related question. This can happen pretty generally, and would probably make more clear the fact that the discussion is carried over from another question (which a plethora of specific tags might not make clear).
I was about to ask a related question:
Shouldn't this series of question appear as a single community-wiki thread?