The boolean hierarchy of NP-partitions

The Boolean Hierar hy of NP - Partitions

Boolean NP-Partitions and Projective Closure

Boolean Hierarchy of Partitions over Reducible Bases

The boolean hierarchy of partitions was introduced and studied by K. Wagner and S. Kosub, mostly over the lattice of NP -sets. We consider this hierarchy for the case of lattices having the reduction property and show that in this case the hierarchy behaves much easier and admits a deeper investigation. We completely characterize the hierarchy over some concrete important lattices, e.g. over th...

A Machine Model for NP-Approximation Problems and the Revenge of the Boolean Hierarchy

This column addresses the following questions about the complexity of approximating the CLIQUE problem. 1. Is nding the vertices of the largest clique more diicult than merely nding the vertices of a 2-approximate clique (that is, a clique with at least half the size of the largest clique)? 2. What computational resources can be used to nd the vertices of a 2-approximate clique? 3. Could fewer ...

Quantum NP and Quantum Hierarchy

The complexity class NP is quintessential and ubiquitous in theoretical computer science. Two different approaches have been made to define “Quantum NP,” the quantum analogue of NP: NQP by Adleman, DeMarrais, and Huang, and QMA by Knill, Kitaev, and Watrous. From an operator point of view, NP can be viewed as the result of the ∃-operator applied to P. Recently, Green, Homer, Moore, and Pollett ...