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check if init(L) is closed or not where init(L) = { w | for some x, wx is in L }

=> Correct if Logic is wrong.

Let there are n differnt state in dfa of L.

Case_1: if len( wx ) >= n and wx is in L then x is either EmptyString or a loop. So deleting that x is Harmless.

Case_2: if len( wx ) < n and wx is in L then either x is EmptyString else whether single ‘w’ reach the final state is undecidable.


So., x is Empty for sure, for all w in init(L) => Closed.
in Theory of Computation 13 points 5 views

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