Bounded Queries and the NP Machine Hypothesis

The NP machine hypothesis posits the existence of an ǫ > 0 and a nondeterministic polynomial-time Turing machine M which accepts the language 0∗ but for which no deterministic Turing machine running in 2nǫ time can output an accepting path infinitely often. This paper shows two applications of the NP machine hypothesis in bounded query complexity. First, if the NP machine hypothesis holds, then PSAT[1] = PSAT[2] =⇒ PH ⊆ NP. Without assuming the NP machine hypothesis, the best known collapse of the Polynomial Hierarchy (PH) is to the class SP 2 due to a result of Fortnow, Pavan and Sengupta [9]. The second application is to bounded query function classes. If the NP machine hypothesis holds then for all constants d > 0, there exists a constant k > d such that for all oracles X, PFSAT[nk ] ⊆ PFX[nd ] . In particular, PFSAT[nd ] PFSAT[nk ] . Without the NP machine hypothesis, there are currently no known consequences even if for all k > 1, PFSAT[nk ] ⊆ PFSAT[n] .

• Type: Conference
• Year: 2007
• Where: COCO
• Authors: Richard Chang, Suresh Purini
• Keywords: COCO 2007, NP Machine Hypothesis, Polynomial-time Turing Machine, Turing Machine