Question

Give regular expressions for the following languages.

(a) ** L₁ = {aⁿbᵐ, n≥3, m≤4}.
(b) L = {aⁿbᵐ : n<4, m≤4}.

Answer 1

To write a regular expression for L₁, use 'a{3,}b{0,4}'. For L, use 'a{0,3}b{0,4}'.

Step-by-step explanation:

To write a regular expression for the language L₁ = {aⁿbᵐ, n≥3, m≤4}, we can break it down into two parts:

1. The part that represents n≥3, where 'a' is repeated at least three times. This can be written as 'a{3,}'.

2. The part that represents m≤4, where 'b' is repeated at most four times. This can be written as 'b{0,4}'.

Combining both parts, the regular expression for L₁ is 'a{3,}b{0,4}'.

For the language L = {aⁿbᵐ : n<4, m≤4}, the regular expression can be written as 'a{0,3}b{0,4}'. Here, 'a' can repeat zero to three times and 'b' can repeat zero to four times.