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Michael Hochman showed that every 1D effectively closed subshift can besimulated by a 3D subshift of finite type and asked whether the same can bedone in 2D. It turned out that the answer is positive and necessary tools werealready developed in tilings theory. We discuss two alternative approaches:first, developed by N. Aubrun and M. Sablik, goes back to Leonid Levin; thesecond one, developed by the authors, goes back to Peter Gacs.

1D Effectively Closed Subshifts and 2D Tilings