Guest Column

Guest Editor's Column

Guest Column: Progress in Descriptive Complexity

The raison d’être of descriptive complexity is the following The Computational Complexity of checking if an input has a property can be understood as the Logical Complexity needed to describe the property. In this guest column I give an overview of descriptive complexity, and survey some current progress and directions. 1 c © Neil Immerman, 2005. Dept. of Computer Science, UMass, Amherst, MA 01...

Guest Column: Small Depth Quantum Circuits1

Small depth quantum circuits have proved to be unexpectedly powerful in comparison to their classical counterparts. We survey some of the recent work on this and present some open problems.

Guest Column: Invitation to Data Reduction and Problem Kernelization1

To solve NP-hard problems, polynomial-time preprocessing is a natural and promising approach. Preprocessing is based on data reduction techniques that take a problem’s input instance and try to perform a reduction to a smaller, equivalent problem kernel. Problem kernelization is a methodology that is rooted in parameterized computational complexity. In this brief survey, we present data reducti...

Guest Column: Completeness in the Polynomial-Time Hierarchy: Part II

In this survey, we highlight selected complete problems from Part I of this column, and include reductions for some of them. We also discuss methods for proving hardness of approximation in the second and higher levels of the Polynomial-Time Hierarchy, and illustrate with two full proofs of non-approximability utilizing error-correcting codes.