# Query: 2018.02.14 VRS Problem 6b: Omega Automata

Hello,

I am not able to figure out why we have taken {{s0},{}} as displayed in right side? Because successor s0 is an acceptance state as displayed in left side. Is there a reason behind it for having such state?

edited
I don't understand your question. Can you explain your doubt in more detail?
Hello Professor,
I want to know why we have {{s0},{ }} state ? My understanding is to consider successor state which are acceptance state in Qf. Here we have a successor s0 which is an acceptance state as well. It should also be in Qf.

Well, when computing the a-successor for ({s0,s2},{s0}), we have to check the a-transitions from states s0 and s2. There is no transition with input a from s0, and from s2, the there is one to state s0. Hence, we get suc∃({s0,s2},a) = {s0} and suc∃({s0},a) = {}, the intersection with the accepting states does not change that, and thus we get state ({s0},{}).
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selected
Thanks for the explanation. It is clear now.