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Referring to the below questions from Exam Paper 2018.02.14 and Exam Paper 2017.08.29 respectively -

In the first question when we are applying Rabin-Scott-Subset-Construction to liveliness automation, we are adding additional state to make it total whereas in the second question, we are not adding any additional state. Why is that so?

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The Rabin-Scott subset construction does not work in general for liveness automata. It does however always work correctly for totally defined liveness automata. That is why we first try to make the liveness automaton totally defined (which however cannot always be done since the nondeterministic version of liveness automata is more powerful than the deterministic one).

Number 2 above refers to the result obtained by the subset construction. Sometimes it is possible that the result is a deterministic prefix automaton, and the number 2 wants you to define a prefix acceptance condition for the result.
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