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* Question: Does the formula have a satisfying assignment of [[Hamming weight]] exactly {{mvar|k}}?
It can be shown that for <math>t\geq2</math> the problem Weighted {{mvar|t}}-Normalize SAT is complete for <math>W[t]</math> under fpt-reductions.<ref>{{cite journal |author=Buss, Jonathan F, Islam, Tarique |title=Simplifying the weft hierarchy |journal=Theoretical Computer Science |year=2006 |volume=351 |number=3 |pages=303–313 |doi=10.1016/j.tcs.2005.10.002|doi-access=free }}</ref>
Here, '''Weighted {{mvar|t}}-Normalize SAT''' is the following problem:
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