Hypercomputation - Taxonomy of "super-recursive" Computation Methodologies

Taxonomy of "super-recursive" Computation Methodologies

Mark Burgin has collected a list of what he calls "super-recursive algorithms" (from Burgin 2005: 132):

• limiting recursive functions and limiting partial recursive functions (E. M. Gold)
• trial and error predicates (Hilary Putnam)
• inductive inference machines (Carl Herbert Smith)
• inductive Turing machines (one of Burgin's own models)
• limit Turing machines (another of Burgin's models)
• trial-and-error machines (Ja. Hintikka and A. Mutanen )
• general Turing machines (J. Schmidhuber)
• Internet machines (van Leeuwen, J. and Wiedermann, J.)
• evolutionary computers, which use DNA to produce the value of a function (Darko Roglic)
• fuzzy computation (Jiří Wiedermann)
• evolutionary Turing machines (Eugene Eberbach)

In the same book, he presents also a list of "algorithmic schemes":

• Turing machines with arbitrary oracles (Alan Turing)
• Transrecursive operators (Borodyanskii and Burgin)
• machines that compute with real numbers (L. Blum, F. Cucker, M. Shub, and S. Smale)
• neural networks based on real numbers (Hava Siegelmann)