Given DFA M accepting a regular language L, we observe that

• is the minimal state DFA accepting L.
• refines , implying
  Each equivalence classes of is the union of some equivalence classes of .
• Hence, each staet of ( which correspond to the equivalence class of ) can be obtained by merging states of M. ( which correspond to equivalence classes of )

But, how do we decide in general when two states can be merged without changing the language accepted?