Question

The “tail” of a language is defined as the set of all suffixes of its strings. That is,

tail(L) = {y : xy ∈ L for some x ∈ Σ∗}

(i). If L = {w ∈ {a, b}∗ : w contains exactly three b’s}, give a brief description of tail(L).

(ii). Show that if L is any regular language, then tail(L) is also a regular language. As with Question 3, you can assume Σ = {a, b} if you like.

*(Hint: There could be various ways to prove this, but the argument I found involves starting with an NFA for L and altering it in a specific way.)

Answer 1

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