OPEN Relationships - Compositions and Containments

Dual Characterizations of Set Containments with Strict Convex Inequalities

Characterizations of the containment of a convex set either in an arbitrary convex set or in the complement of a …nite union of convex sets (i.e. the set, described by reverse-convex inequalities) are given. These characterizations provide ways of verifying the containments either by comparing their corresponding dual cones or by checking the consistency of suitable associated systems. The conv...

On perfect completeness for QMA

Whether the class QMA (Quantum Merlin Arthur) is equal to QMA1, or QMA with onesided error, has been an open problem for years. This note helps to explain why the problem is difficult, by using ideas from real analysis to give a “quantum oracle” relative to which QMA 6= QMA1. As a byproduct, we find that there are facts about quantum complexity classes that are classically relativizing but not ...

Cracking of Prestressed Concrete Containments

A Deterministic Approach to XML Query Processing with Efficient Support for Pure and Negated Containments

This article reports the result of the author’s recent work on XML query processing/optimization, which is a very important issue in XML data management. In this work, in order to more effectively and efficiently handle XML queries involving pure and/or negated containments, a previously proposed deterministic optimization approach is largely adapted. This approach resorts to heuristic-based de...

The Tree Evaluation Problem: Towards Separating P from NL

As of today, we do not know if even one among the above sequence of containments is strict. In fact, it is open if AC(6)=PH ! In this lecture by Steve we learn about an attempt aimed at separating P from NL using a specific problem called the Tree Evaluation Problem. Most of the contents of the talk are derived from the work “Pebbles and Branching Programs for tree evaluation” [1] by Steve Cook...