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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 =
We know that the intersection of SL2 languages is also SL2. If the complement of SL2 languages was also necessarily SL2, then 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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While the SL 2 languages include some surprisingly complex languages, the strictly 2-local automata are, nevertheless, quite limited. In a strong sense, they are almost memoryless
The key thing about the Suffx Substitution Closure property is that it does not make any explicit reference to the automaton that recognizes the language. While the argument tha
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The fact that regular languages are closed under Boolean operations simpli?es the process of establishing regularity of languages; in essence we can augment the regular operations
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