I recently submitted a paper to a conference whose notification of acceptance/rejection is due to 3 months from now. However I realize that I can extend my results in such a way that it gets much more general and such that the results of the previous paper follows as a special case. The generalization however is non-trivial, in the sense that I will need much more advanced and esoteric techniques, and somewhat more 20 pages to write it properly. It also fits in the scope of a conference whose deadline is in 2 months. Here are my options.
1) Put the first paper at arxiv. Write the second paper citing it and showing where things get different. Submit the second paper. But then the second paper doesn't get self contained enough.
2) Put the first paper at arxiv. Make the second paper self contained by rewriting all results that I need from the first one, but specifying that it is a generalization of the first one. Submit the second paper.
3) Write the second paper and wait for the result of the first conference. If accepted, write the second paper as an independent extension of the first one. If rejected, merge everything into a new piece of work and resubmit to a new conference whose deadline is in 5 months.
a) There are two groups working in a very related subject, and I'm afraid putting the first paper in arxiv would lead them to a similar generalization before me. So I wonder If I should wait to put the first paper on arxiv until having finished the second one.
b) If I write the second paper and put it at arxiv before the notification from the conference, could this make the first paper be rejected because the program committee would argue that there is a possible generalization of it? Even though highly non-trivial?
c) If I submit the second paper to a new conference but don't put it on arxiv, would I fall in the case of double submission?
What is the best way to proceed in this case? I believe several researchers might have faced similar situations.