Consider the language \(L=\left\{a^{n} b^{m}: n \geq 4, m \leq 3\right\}\)…

Final regular expression: a^4 a* (λ + b + bb + bbb)

• Ensure at least four a's: write a^4 then allow extra a's with a* to get a^4 a*.

• Allow 0 to 3 b's: use (λ + b + bb + bbb), which explicitly includes the empty string and 1–3 b's.

• Combine both parts to get the language { a^n b^m : n ≥ 4, m ≤ 3 }: a^4 a* (λ + b + bb + bbb).

Equivalent compact forms: a^4 a* b^{0,3} or a^{4,} b^{0,3} (meaning at least four a's, followed by 0 to 3 b's).

Examples accepted by this expression: aaaa, aaaaa, aaaa b, aaaaa bbb.

Examples rejected: aaa (too few a's), aaaa bbbb (too many b's).