Real Recursive Functions and Real Extensions of Recursive Functions

Recently, functions over the reals that extend elementarily computable functions over the integers have been proved to correspond to the smallest class of real functions containing some basic functions and closed by composition and linear integration. We extend this result to all computable functions: functions over the reals that extend total recursive functions over the integers are proved to correspond to the smallest class of real functions containing some basic functions and closed by composition, linear integration and a very natural unique minimization schema.

• Type: Conference
• Year: 2004
• Where: MCU
• Authors: Olivier Bournez, Emmanuel Hainry
• Keywords: Basic Functions, Computable Functions, MCU 2004, MCU 2007, Real Functions