An analysis of the W*-hierarchy


We observe that the W∗-hierarchy, a variant (introduced by Downey, Fellows, and Taylor [8]) of the better known W-hierarchy, coincides with the W-hierarchy, though not level wise, but just as a whole hierarchy. More precisely, we prove that W[t] ⊆ W∗[t] ⊆ W[2t − 2] for each t ≥ 2. It was known before that W[1] = W∗[1] and W[2] = W∗[2]. Our second main… (More)