prove that the language = { ∈ Σ∗|∀1 ≤ ≤ : #() ≤ }, where is defined over Σ = { | 1 ≤ ≤ } is regular using Nerode law. basically the string w has, at most, occurrences of the letter at index in Σ for each 1 ≤ ≤ .
The main problem I have is to defining the equivalent classes.
I'd like to ask for help in defining the equivalent classes, and showing that no string belongs to more than one equivalent class. if there's an intuition for it, I'd love to hear that as well.
Thank you.