Question

For given Σ{{a,b}, define a language where there are odd number of "a"s in the string.

Answer 1

The question asks to define a language over the alphabet Σ = {a,b} with an odd number of "a"s in the string. The language can be described by a regular expression that ensures an odd count of "a"s by starting and ending with an "a" and allowing any number of "b"s or "aa" pairs in between. Example strings would include "a", "aba", "abba", "aaab", etc.

Step-by-step explanation:

To define a language where there is an odd number of "a"s in a string over the alphabet Σ = {a,b}, we need to create a set of rules that allow for any string that has a count of "a"s that is not divisible by 2. This could mean one "a", three "a"s, five "a"s, and so on. The language can be represented by the regular expression a(b|a[ᵃ])*a, where we ensure that there's at least one "a" at the beginning and at the end of the string, and between them can be any number of "b"s or pairs of "a"s that do not disrupt the odd count of "a"s.

The set of strings that belong to this language includes "a", "aba", "abba", "ab", etc., with the key point being that between any two "a" characters, there can be any number of "b"s or pairs "aa" (since a pair does not change the parity of the count of "a"s). To clarify further, here is an example string that confirms the rule: baa baa. This string has exactly five "a"s which is an odd number.

Answer 2

A language with an odd number of 'a's over the alphabet {a, b} can be defined using regular expressions, such as (b*ab*a)*ab*, which allows for any number of 'b's between 'a's and ensures an odd number of 'a's in the string.

Step-by-step explanation:

Defining a Langu:age with Odd Numbers of 'a'

To define a language over the alphabet Σ = {a, b} that includes strings with an odd number of 'a's, you can describe it with the help of regular expressions or by providing a set of rules. For example, any string that follows a pattern where 'a' is surrounded by any number of 'b's, including zero, but ensuring that 'a' appears an odd number of times, would belong to this language.

A simple regular expression for this language might be: (b*ab*a)*ab* which denotes strings where 'a' is always in the middle of any number of 'b's with at least one 'a' guaranteed to appear and where the occurrences of 'a' are odd in number.