Using approximation to characterize real computable functions
In this talk the method of approximation to relate various classes of computable functions over the reals is reviewed. Using this method, Computable Analysis will be compared to two analog models: the
General Purpose Analog Computer and Real Recursive Functions. There are a number of existing results in the literature showing that the different models correspond exactly. It will be shown that those exact correspondences can be broken down into a two step process of approximation and completion. The method of approximation has further application in relating classes of functions, exploiting the transitive nature of the approximation relation. As an example, it will be shown how to eliminate non-analytic functions from the previously known analog characterization of the real elementary computable functions.
Join work with Kerry Ojakian (IST/UTL and SQIG/IT).
Areas of interest
Logic and Computation
Manuel Campagnolo (DM/ISA/UTL e SQIG/IT)
December 17, 2007