Separating Complexity Classes Using Structural Properties

We study the robustness of complete sets for various complexity classes. A complete set A is robust if for any f(n)-dense set S ∈ P, A−S is still complete, where f(n) ranges from log(n), polynomial, to subexponential. We show that robustness can be used to separate complexity classes: • for every ≤p m-complete set A for EXP and any subexponential dense sets S ∈ P, A − S is still Turing complete and under a reasonable hardness assumption even ≤p m-complete. • For EXP and the delta levels of the exponential hierarchy we show that for every Turing complete set A and any log-dense set S ∈ P, A − S is still Turing complete. • There exists a 3-truth-table complete set A for EEXPSPACE, and a log-dense set S ∈ P such that A − S is not Turing complete. This implies that settling this issue for EEXP will either separate P from PSPACE or PH from EXP. • We show that the robustness results for EXP and the delta levels of the exponential hierarchy do not relativize.

• Type: Conference
• Year: 2004
• Where: COCO
• Authors: Harry Buhrman, Leen Torenvliet
• Keywords: COCO 2004, Complete Set, Complexity Classes, Turing Complete