Let swap_every_two be an operation on languages that is defined as follows: swap_every_two(L) = {a2a1a4a3 ....

Let swap_every_two be an operation on languages that is defined as follows:

swap_every_two(L) = {a2a1a4a3 . . . a2na2n−1 | a1a2a3a4 . . . a2n−1a2n ∈ L where a1, . . . , a2n ∈ Σ} In this definition, Σ is the alphabet for the language L. (it is a2a1a4a3 not a^2a^1 !!)

1. What languages result from applying swap_every_two to the following languages:

(a) {1^n | n ≥ 0}, where the alphabet is {1}.

(b) {(01)^n | n ≥ 0}, where the alphabet is {0, 1}.

2. Show that if L is a regular language then so it swap every two(L).

Expert Solution

venereology answered 5 months ago

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