Deterministic coloring of a family of complexes

This is the second paper devoted to construction of finitely presented infinite nil semigroup with identity $x^9=0$. This construction answers to the problem of Lev Shevrin and Mark Sapir. In the first part we constructed the sequence of complexes with some set of properties. Namely, all these complexes are uniform elliptic: any two points $A$ and $B$ with distance $d$ can be connected with a system of shortest paths forming a disk of width $λ\cdot D$ for some global constant $λ> 0$. In the second part of the proof, a finite system of colors with determinism is introduced: for each minimum square that the complex consists of, the color of the three angles determines the color of the fourth corner. The present paper is devoted to the second part of the proof.

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