Regular Expression for Odd Sum of {a^n b^m}

What is a regular expression for the set {a^n b^m : (n + m) is odd}?

Can you provide an example to explain the concept better?

Regular Expression and Example

The regular expression for the set {a^n b^m : (n + m) is odd} would be (a+)(b+).

Let's consider an example to understand this concept better. Suppose we have the string "aaab". In this case, n=3 and m=1.

In the given example, the substring "a" occurs three times and the substring "b" occurs once, resulting in an odd sum of 4.

Therefore, the regular expression (a+)(b+) matches this string, as it contains at least one "a" and one "b" with an odd total count of letters.

Conversely, if we take a string like "aab", the total number of letters is even because there are two "a"s and one "b". This sums up to three, an odd number.

As a result, (a+)(b+) will not match the string "aab" as it fails to meet the condition of having an odd sum of n and m.

To delve deeper into regular expressions and their applications, you can explore more resources on the topic.