No wonder you activities are, reading will be always needed. It is not only to fulfil the duties that you need to finish in deadline time. Reading will encourage your mind and thoughts. Of course, reading will greatly develop your experiences about everything. Reading tractability practical approaches to hard problems is also a way as one of the collective books that gives many advantages. The ...

Group and individual solutions are considered for hard problems such as satisfiability problem. Time-space trade-off in a structured active memory provides means to achieve lower time complexity for solutions of these problems.

Complexity theory provides a wealth of complexity classes for analyzing the complexity of decision and counting problems. Despite the practical relevance of enumeration problems, the tools provided by complexity theory for this important class of problems are very limited. In particular, complexity classes analogous to the polynomial hierarchy and an appropriate notion of problem reduction are ...

Existing models for sampling the space of all planning problems produce both solvable and unsolvable instances. In particular, when attempting to identify very hard ones, one encounters both, as the hardness in the standard models is accompanied by the possibility of an instance being solvable or unsolvable. This is a disadvantage of the standard models, because of the strong asymmetry of plann...

We introduce captcha, an automated test that humans can pass, but current computer programs can’t pass: any program that has high success over a captcha can be used to solve an unsolved Artificial Intelligence (AI) problem. We provide several novel constructions of captchas. Since captchas have many applications in practical security, our approach introduces a new class of hard problems that ca...

Modern cryptography has had considerable impact on the development of computational learning theory. Tools from cryptography have been used in proving nearly all of the strong negative results for learning. In this paper, we give results in the reverse direction by showing how to construct several cryptographic primitives based on certain assumptions on the di culty of learning. Thus we develop...

ix Title: Statistical Physics of Hard Optimization Problems Author: Lenka Zdeborová Abstract: Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a cost function depending on these variables. Optimization problems ...

The field of exact exponential time algorithms for NP-hard problems has thrived over the last decade. While exhaustive search remains asymptotically the fastest known algorithm for some basic problems, difficult and non-trivial exponential time algorithms have been found for a myriad of problems, including Graph Coloring, Hamiltonian Path, Dominating Set and 3-CNF-Sat. In some instances, improv...

The knapsack problem is believed to be one of the “easier” N P -hard problems. Not only can it be solved in pseudo-polynomial time, but also decades of algorithmic improvements have made it possible to solve nearly all standard instances from the literature. The purpose of this paper is to give an overview of all recent exact solution approaches, and to show that the knapsack problem still is h...

We present the latest instantiation of GridSAT [5], a distributed and complete satisfiability solver that is explicitly designed to aggregate grid resources for application performance. GridSAT was previously shown to outperform the state-of-the-art sequential solvers. In this work, we explore the unprecedented solving power GridSAT enables through algorithmic and implementation innovations. We...