The Domino Problem of the Hyperbolic Plane Is Undecidable: New Proof

Abstract

The present paper revisits the proof given in a paper of the author published in 2008 proving that the general tiling problem of the hyperbolic plane is algorithmically unsolvable by proving a slightly stronger version using only a regular polygon as the basic shape of the tiles. The problem was raised by a paper of Raphael Robinson in 1971, in his famous simplified proof that the general tiling problem is algorithmically unsolvable for the Euclidean plane, initially proved by Robert Berger in 1966. The present construction improves that of the 2008 paper. It also very strongly reduces the number of prototiles.