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 ...

Abstract: Concurrent interprocedural program analysis is an undecidable problem. To analysis concurrent interprocedural program, we need understand why the problem is undecidable. [1] proofs the ...

The world of mathematics is full of unreachable corners, where unsolvable problems live. Now, yet another has been exposed. In 1900, the eminent mathematician David Hilbert announced a list of 23 key ...

The spectral gap - the energy difference between the ground state and first excited state - is central to quantum many-body physics. Many challenging open problems, such as the Haldane conjecture, ...

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 ...

A logical paradox at the heart of mathematics and computer science turns out to have implications for the real world, making a basic question about matter fundamentally unanswerable. In 1931, Austrian ...

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, ...