In this paper we study generic complexity of undecidable problems. It turns out that some classical undecidable problems are, in fact, strongly undecidable, i.e., they are undecidable on every ...

The Post Correspondence Problem is an undecidable problem in which you’re given two lists of strings, and the goal is to find a sequence of indices such that the concatenated strings from both lists ...

Abstract: This paper describes some general results about hierarchies of undecidable problems in automata theory, and studies how properties of sets accepted by automata change from decidable to ...

The Post Correspondence Problem (PCP) is an undecidable problem. It asks whether a set of domino-like pairs of strings can be arranged in a sequence so that the top and bottom strings match. There's ...

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 ...

Variational Quantum Algorithms (VQAs) are prime candidates for near-term quantum advantage, yet training them is known to be NP-hard. Here we prove a conditional undecidability result for noiseless, ...

A mathematical problem underlying fundamental questions in particle and quantum physics is provably unsolvable, according to scientists at UCL, Universidad Complutense de Madrid - ICMAT and Technical ...