Marvin L. Minsky, Recursive Unsolvability of Post's Problem of "Tag" and other Topics in Theory of Turing Machines, Annals of Mathematics, Vol. 74, No. 3 (Nov., 1961), pp. 437-455 ...

And Kurt Gödel worked on the incompleteness theory and recursive function theory. Turing employed the work of both mathematicians to create a conceptual computing machine.

Our point of view is that Kleene's (second) recursion theorem is essential to understand self-replication mechanisms. An interesting example of self-replication codes is given by computer viruses.

Such is Turing's legacy: that of a nested chain of pretenses, each pointing not to reality, but to the caricature of another idea, device, individual, or concept.

As increasingly sophisticated models like ChatGPT test the boundaries of machine intelligence – the potential consequences for society are profound. As artificial intelligence, AI, continues its rapid ...