We give a proof of Ollinger's conjecture that the problem of tiling the plane with translated copies of a set of $8$ polyominoes is undecidable. The techniques employed in our proof include a different orientation for simulating the Wang tiles in polyomino and a new method for encoding the colors of Wang tiles.

翻译：我们给出了奥林格猜想的一个证明，即用一组$8$个多联骨牌平移复制品铺满平面的问题是不可判定的。证明中采用的技术包括：在多联骨牌中模拟王瓷砖的不同定向方法，以及一种编码王瓷砖颜色的新方法。