Class Description

AW[SAT]: Alternating W[SAT]

Basically has the same relation to W[SAT] as PSPACE does to NP.

The class of decision problems of the form (x,r,k₁,...,k_r) (r,k₁,...,k_r parameters), that are fixed-parameter reducible to the following problem, for some constant h:

Parameterized QBFSAT: Given a Boolean formula F (with no restriction on depth), over disjoint variable sets S₁,...,S_r. Does there exist an assignment to S₁ of Hamming weight k₁, such that for all assignments to S₂ of Hamming weight k₂, etc. (alternating 'there exists' and 'for all'), F is satisfied?

See W[1] for the definition of fixed-parameter reducibility.

Defined in [DF99].

Contains AW[*], and is contained in AW[P].

Linked From

AW[P]: Alternating W[P]

Same as AW[SAT] but with 'circuit' instead of 'formula.'

Has the same relation to AW[SAT] as W[P] has to W[SAT].

Defined in [DF99].

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AW[t]: Alternating W[t]

Has the same relation to W[t] as PSPACE does to NP.

Same as AW[SAT], except that the formula F can have depth at most t.

Defined in [DF99].

Contained in AW[*].

[DFT98] show that for all t, AW[t] = AW[*].

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