Complexity of approximately solved problems

Solved and unsolved problems in generalized notions of Connes amenability

We survey the recent investigations on (bounded, sequential) approximate Connes amenability and pseudo-Connes amenability for dual Banach algebras. We will discuss the core problems concerning these notions and address the signicance of any solutions to them to the development of the eld.

The Complexity of Approximately Solving Influence Diagrams

Influence diagrams allow for intuitive and yet precise description of complex situations involving decision making under uncertainty. Unfortunately, most of the problems described by influence diagrams are hard to solve. In this paper we discuss the complexity of approximately solving influence diagrams. We do not assume no-forgetting or regularity, which makes the class of problems we address ...

The Complexity of Approximately Counting Stable Matchings

We investigate the complexity of approximately counting stable matchings in the k-attribute model, where the preference lists are determined by dot products of “preference vectors” with “attribute vectors”, or by Euclidean distances between “preference points“ and “attribute points”. Irving and Leather [16] proved that counting the number of stable matchings in the general case is #P -complete....

Solved Problems in Random Processes

On Generating Solved Instances of Computational Problems

We consider the e cient generation of solved instances of computational problems. In particular, we consider invulnerable generators. Let S be a subset of f0; 1g and M be a Turing Machine that accepts S; an accepting computation w of M on input x is called a \witness" that x 2 S. Informally, a program is an -invulnerable generator if, on input 1 n , it produces instancewitness pairs hx; wi, wit...