The Euclid Abstract Machine
Jerzy Mycka, José Félix Costa and Francisco Coelho
Concrete non-computable functions are usually related to the halting function. Is it possible to present examples of non-computability, which are unrelated to the halting problem and its derivatives? We built an abstract machine based on the historic concept of compass and ruler constructions (a compass construction would suffice) which reveals the existence of non-computable functions not related with the halting problem. These natural, and the same time, non-computable functions can help to understand the nature of the uncomputable and the purpose, the goal, and the meaning of computing beyond Turing.