Deciding if a homshift is Θ(n)-block gluing is undecidable via reduction to finiteness of finitely presented groups using topological interpretation of square covers.
Blondel, Quasi-periodic configurations and undecidable dynamics for tilings, infinite words and T uring machines , Theoretical Computer Science 319 (2004), no
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Undecidability of the block gluing classes of homshifts
Deciding if a homshift is Θ(n)-block gluing is undecidable via reduction to finiteness of finitely presented groups using topological interpretation of square covers.