I'm doing a problem where I need to find the $≡_A$ equivalence classes of the language $$A = \{ 0^{n}x \mid n \in \mathbb Z^+, x \in \{0, 1\}^*, \text{ and } \#_0(x) ≥ n \}. $$
The best way I've learned to find the equivalence classes from a formal language is to create an automation and minimize it. Is there a conventional way of finding the equivalence classes of a language more quickly and intuitively? Because I do not know the DFA for this problem. Thanks for the help!