We prove that certain problems naturally arising in knot theory are NP–hard or NP–complete. These the of obtaining one diagram from another a link bounded number Reidemeister moves, determining whether has an unlinking splitting k <mml:annotation enc...

Several physically inspired problems have been proven undecidable; examples are the spectral gap problem and membership for quantum correlations. Most of these results rely on reductions from a handful undecidable problems, such as halting problem, tiling Post correspondence or matrix mortality problem. All common property: they an NP-hard bounded version. This work establishes relation between...