The equivalence of theorem proving and the interconnection problem

Abstract

A simple method of converting statements in mathematical logic to equivalent interconnection problems is demonstrated. This shows that if there exists a practical method for solving interconnection problems, then there exists a practical proof procedure for statements in mathematical logic. (In the terminology of Cook [1] and Karp [4], the interconnection problem is NP-complete.) Since such a procedure has been sought for without success for almost 100 years, we should not expect the interconnection problem to be any easier. This holds equally true for finding a method which will route a given percentage of wires.