Let L be a language over the alphabet {a, b} such that L = { w ∈ {a, b} | w…

The language L is regular. To justify this, we analyze the relationship between the counts of substrings "ab" and "ba". These substrings represent transitions between different characters in the string. Specifically, every occurrence of "ab" corresponds to a switch from 'a' to 'b', and "ba" corresponds to a switch from 'b' to 'a'. For the counts to be equal, the number of switches from 'a' to 'b' must exactly equal the number of switches from 'b' to 'a'. This condition holds if and only if the string starts and ends with the same character, or if the string is empty or a single character where no transitions occur. Consequently, L can be described by the regular expression a(a+b)*a U b(a+b)*b U {epsilon, a, b}. This property allows us to define the language using simple concatenation and union operations. Since a regular expression exists for L, the language is regular. All regular languages are also context-free, but regular is the strongest classification. A deterministic finite automaton (DFA) can be constructed with states tracking the first character and the current character to verify the start and end match. Thus, L is regular.