The 4-way deterministic tiling problem is undecidable

The 4-way deterministic tiling problem is undecidable

It is shown that the (infinite) tiling problem byWang tiles is undecidable even if the given tile set is deterministic by all four corners, i.e. a tile is uniquely determined by the colors of any two adjacent edges. The reduction is done from the Turing machine halting problem and uses the aperiodic tile set of Kari and Papasoglu. © 2008 Elsevier B.V. All rights reserved.

The Finite Tiling Problem is Undecidable in the Hyperbolic Plane

In this paper, we consider the nite tiling problem which was proved undecidable in the Euclidean plane by Jarkko Kari, see [4]. Here, we prove that the same problem for the hyperbolic plane is also undecidable.

Whitehead's Problem is Undecidable

The Neural Network Loading Problem Is Undecidable

There exist several well known results concerning the computational complexity of training, design, etc. of (artiicial) neural networks which demonstrated that these problems are at least NP complete. Extending these results we will prove here that the training of neural networks, i.e. the so called \loading problem", in general, is even \unsolvable". This implies in particular that there exist...

The Hurwitz Equivalence Problem Is Undecidable

In this paper, we prove that the Hurwitz equivalence problem for 1-factorizations in F2⊕F2 is undecidable, and as a consequence, the Hurwitz equivalence problem for ∆-factorizations in the braid groups Bn, n ≥ 5 is also undecidable.