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Closure Properties of Regular Languages If L is a regular language

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   Closure Properties of Regular Languages
If L is a regular language, then so are:
L, L∗, and LR.
Closure under homomorphism.
Let Σ and Γ be alphabets.
Let h be a function h : Σ → Γ∗
Define h(λ) = λ, and h(aw) = h(a) · h(w)
Define h(L) = {w : w = h(w), w ∈ L}
If L is a regular language, then so is h(L).

If L1 and L2 are regular languages, then so are:
   L1 ∪ L2
   L1 ∩ L2
   L1L2 = {xy : x ∈ L1, y ∈ L2}
   L1/L2 = {x : xy ∈ L1, y ∈ L2}
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Computational Properties of Regular Languages
Let w be a string. Let L, L1, and L2 be lan-
guages represented as DFAs, NFAs, regular ex-
pressions, or regular grammars.
There are efficient algorithms to determine if
w ∈ L.
There are efficient algorithms to determine if L
is empty, finite, or infinite.
There are algorithms to determine if L1 = L2,
efficient for DFA representation.

								
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