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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 .
Construct a Mealy machine that can output EVEN or ODD According to the total no. of 1''s encountered is even or odd.
a) Let n be the pumping lemma constant. Then if L is regular, PL implies that s can be decomposed into xyz, |y| > 0, |xy| ≤n, such that xy i z is in L for all i ≥0. Since the le
Intuitively, closure of SL 2 under intersection is reasonably easy to see, particularly if one considers the Myhill graphs of the automata. Any path through both graphs will be a
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how to convert a grammar into GNF
dfa for (00)*(11)*
Both L 1 and L 2 are SL 2 . (You should verify this by thinking about what the automata look like.) We claim that L 1 ∪ L 2 ∈ SL 2 . To see this, suppose, by way of con
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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