All Questions

I call an H-machine a machine that can be connected to turing machines and that takes as input a natural integer n and instantly returns the n'th digit of the mathematical constant H. Is there a ...

Background By the MRDP theorem, every for every recursively enumerable set $S$, there exists a Diophantine polynomial $p$ such that $$x \in S \iff \exists y_1, \dots, y_n \in \mathbb{N} \text{ such ...

If I had access to potentially unlimited CPUs and wanted to quickly check 100 million digit numbers for primality using a map-reduce architecture, how many CPUs would be necessary? Each of the mapped ...