Review of equivalence relations. State reduction technique based on the equivalence relation on a DFA of the Myhill-Nerode Theorem: Two states A,B of a DFA are equivalent if the sets of strings accepted from A and B are equal. If two states are equivalent under the above definition, then you can merge them in the obvious way. Let L be a regular language over an alphabet Σ . Equivalence relation on Σ * : Two strings u,v are equivalent if for all strings w, uw ∈ L iff vw ∈ L. We will take the following as fact (i.e. we will not cover the proof): the number of equivalence classes is equal to the number of states in a smallest DFA accepting L.