Testing k-binomial equivalence

Two words w1 and w2 are said to be k-binomial equivalent if every non-empty word x of length at most k over the alphabet of w1 and w2 appears as a scattered factor of w1 exactly as many times as it appears as a scattered factor of w2. We give two different polynomial-time algorithms testing the k-binomial equivalence of two words. The first one is deterministic (but the degree of the corresponding polynomial is too high) while the second one is randomised (but more direct and efficient).