Quantitative Computation by Hilbert Machines

摘要

In order to extend classical models of computing with symbols we introduce a model for quantitative computation which is based on infinite-dimensional topological linear structures. In particular machines which operate on data taken from Hilbert spaces will be looked at. These Hilbert machines (and other topological linear machines) allow the adequate treatment of concepts like infiniteness and similarity as they are based on a combination of a simple algebraic structure together with a topological one.