I have read a lot of books on membrane computing (P system), of which the computational completeness of several variants are already under investigation. My goal is to design my own variant and prove its computational completeness.
I also know that in order to prove computational completeness many research papers normally prove the equivalence of their variants of P system with variants of formal languages (e.g. context-free, context sensitive languages, Turing machines etc.), those of which are already known to be computationally complete.
My question is how exactly can I prove equivalence of a variant of P system with a formal language?