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Time-Space Lower Bounds for the Polynomial-Time Hierarchy on Randomized Machines
[chapter]

2005
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Lecture Notes in Computer Science
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We establish the first polynomial-strength time-space lower bounds for problems in the lineartime hierarchy on randomized machines with two-sided error. We show that for any integer ℓ > 1 and constant c < ℓ, there exists a positive constant d such that QSAT ℓ cannot be computed by such machines in time n c and space n d , where QSAT ℓ denotes the problem of deciding the validity of a quantified Boolean formula with at most ℓ − 1 quantifier alternations. Moreover, d approaches 1/2 from below as

doi:10.1007/11523468_79
fatcat:tu7eceadn5flpcszt37wg7tzwu