1) For Non-Deterministic liveness automat, when to use subset and when to use breakpoint construction.

As per my understanding, non-deterministic partial liveness automata shall be converted into prefix non-deterministic liveness automata and then use subset construction to determinize, right?

But in slides it is also mentioned that non-deterministic liveness automata will go to non-deterministic co-buchi and then finally into deterministic co-buchi using breakpoint. so in this case, what shall be used to convert non-deterministic liveness to non-deterministic co-buchi?

I am confused for liveness automat when to use what?

Please explain