I'm writing a paper on an extension of a topic I investigated in my PhD thesis. The paper refines what is known about a particular (automaton) model, call it A. I find the paper interesting. On the one hand, it uses classical results from a theoretical field (logic) and applies it to a practical problem. On the other hand, the solution is not completely straightforward. In fact, I came back to this problem after not having been able to solve it months ago.
Now, a researcher in my thesis committee sent me a paper discussing another model, let's call it B. It seems that B is more general than A but for that reason the properties one can prove about B are not as strong. Still there seems to be a transfer of ideas I used in my thesis in the study of B. The paper contains a number of "open problems". It also provides motivating material to continue developing my paper on model A.
I'm working alone on this problem and preparing simultaneously a grant application finishing in two months.
Question
Should I stop writing my paper on A and understand the unclear points in B? Should I keep writing my paper on A borrowing ideas from the development in B and stating that they motivated the questions I ask about A? In the latter case, should I defer the publication of A until I try the problems in B to avoid not solving the problems in B with the new techniques I come up for A?
I can work on a paper and a grant writing simultaneously but more would be difficult. Ideally, I should have the support of master students or my PhD advisor. But he left me on my own for the whole degree.
