Well, the simplest way is that you would have to list all transitions as minterms of a DNF. It would start like this:

!p&!q&!Xp&!Xq | !p&!q&!Xp&Xq | ...

You could generate the associated Kripke structure, but that is just more work and you will get the same formula as the one above. So, that is not useful.

The acceptance condition is the set of gray states (I guess) which is

p&q

but from the diagram, we don't know whether that is a safety, liveness or whatever automaton.