for a language L over Σ, u =N u′
if, for all w in Σ*, uw ∈ L iff u′w ∈ L
and for a function f, u =N u′
if, for all w in Σ*, f(uw) = f(u′w)
Although coarser than the Myhill equivalence, it is finite only if the latter is. Unlike the latter, it gives only a right congruence: u =N u′ implies uv =N u′v
and thus does not give rise to a semigroup. The number of equivalence classes is the number of states in the minimal machine for L.
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