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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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Given any NFA A, we will construct a regular expression denoting L(A) by means of an expression graph, a generalization of NFA transition graphs in which the edges are labeled with
The k-local Myhill graphs provide an easy means to generalize the suffix substitution closure property for the strictly k-local languages. Lemma (k-Local Suffix Substitution Clo
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This was one of the ?rst substantial theorems of Formal Language Theory. It's maybe not too surprising to us, as we have already seen a similar equivalence between LTO and SF. But
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The generalization of the interpretation of strictly local automata as generators is similar, in some respects, to the generalization of Myhill graphs. Again, the set of possible s
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