Abstract: The purpose of this paper is to gain a better understanding of the structure of undecidable problems in automata theory by investigating the degree of unsolvability of these problems. This ...

This project presents an exploration into Alan Turing's Halting Problem, providing a solution using ordinal arithmetic and trigonometric recursion. It builds on the principles of Turing machines, ...

The original version of this story appeared in Quanta Magazine. The world of mathematics is full of unreachable corners, where unsolvable problems live. Now, yet another has been exposed. In 1900, the ...

In this work, we show that very natural, apparently simple problems in quantum measurement theory can be undecidable even if their classical analogues are decidable. Undecidability hence appears as a ...

Seventh Workshop on Resiliency in High Performance Computing with Clouds, Grids, and Clusters problems in presence of a general class of faults are undecidable, that is, no algorithms exist for ...

Are all problems in mathematics solved? The answer is no. There are several that remain unproven, even with most mathematicians and computer scientists having a common idea about it. Time complexity, ...