CRITICAL POINTS IN THE HISTORY OF SUPER-RECURSIVE ALGORITHMS



 

1965 - first published description of super-recursive algorithms:
            limiting recursive and limiting partial recursive functions                                              (M.E. Gold, H. Putnam)
 

1974 - first published description of an abstract device (Turing machine)
             for realization of super-recursive algorithms                                                      (R.V. Freuvald)
 

1983 - introduction of an inductive Turing machine with a structured memory
             that are much more powerful than all previous models                                             (M. Burgin)
 

1987-8 - theorem on super-recursive representation of the arithmetical hierarchy being
                published and its implications for the first Gödel incompleteness theorem considered       (M. Burgin)
 

1992 - implementation of topological principles in the theory of super-recursive algorithms:
             introduction of a limit Turing machine with a structured memory                             (M. Burgin)
 

1998-9 - proof of the results demonstrating that efficiency of the super-recursive
              algorithms is much higher than efficiency of the recursive algorithms                                  (M. Burgin)