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→W hierarchy: Standard definition of W[1] (*exactly* k 1s, not *at most* k 1s.) Also, kill a “wicked which”. |
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=== ''W'' hierarchy ===
The '''''W'' hierarchy''' is a collection of computational complexity classes. A parameterized problem is in the class ''W''[''i''], if every instance <math>(x, k)</math> can be transformed (in fpt-time) to a combinatorial circuit that has [[weft (circuit)|weft]] at most ''i'', such that <math>(x, k)\in L</math> if and only if there is a satisfying assignment to the inputs
Note that <math>\mathsf{FPT} = W[0]</math> and <math>W[i] \subseteq W[j]</math> for all <math>i\le j</math>. The classes in the ''W'' hierarchy are also closed under fpt-reduction.
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