W e propose a weak version of the Blum-Shub-Smale model of computation over the real numbers. In this weak model only a “moderate” usage of multiplicat ions and divisions is allowed. The class of languages recognizable in polynomial tine is shown t o be the complexity class P/poly . This implies under a standard complexity-theoretic assumption that P#NP in the weak model, and that problems such as the real traveling salesman problem cannot be solved in polynomial t ime. A s an application, we… CONTINUE READING