Complement - operations on languages, Theory of Computation

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The fact that SL2 is closed under intersection but not under union implies that it is not closed under complement since, by DeMorgan's Theorem

L1 ∩ L2 = 412_lema.png

We know that the intersection of SL2 languages is also SL2. If the complement of SL2 languages was also necessarily SL2, then 412_lema.png would be SL2 contradicting the fact that there are SL2 languages whose union are not SL2.

Lemma The class of strictly 2-local languages is not closed under complement .


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