Preprocessing of Intractable Problems

Preprocessing of Intractable Problems

Some computationally hard problems –e.g., deduction in logical knowledge bases– are such that part of an instance is known well before the rest of it, and remains the same for several subsequent instances of the problem. In these cases, it is useful to preprocess off-line this known part so as to simplify the remaining on-line problem. In this paper we investigate such a technique in the contex...

Intractable Problems in Cryptography

We examine several variants of the Diffie-Hellman and Discrete Log problems that are connected to the security of cryptographic protocols. We discuss the reductions that are known between them and the challenges in trying to assess the true level of difficulty of these problems, particularly if they are interactive or have complicated input.

Timing Matters: Tackling Intractable Problems

I f you were at least five years old on 20 July 1969, then you know exactly where you were when Neil Armstrong became the first human to walk on the moon. With that act, America won the space race. Safely going to and returning from the moon was a long-term goal that required solving a myriad of related technical problems. It took concerted resolve to overcome this heretofore intractable scient...

Computationally Intractable Problems in Communications

The theory of NP-completeness deals with problems for which we do not know a deterministic algorithm for finding the solution in an amount of time polynomial in the size of the input. These problems—belonging to the set N P-complete—are of great practical importance because they arise naturally in numerous decision and optimization problems [Baas]. Yet, no one has shown whether such problems ca...

Average-Case Intractable NP Problems