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The Domino Problem for Self-similar Structures

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 9709)


We define the domino problem for tilings over self-similar structures of \(\mathbb {Z}^d\) given by forbidden patterns. In this setting we exhibit non-trivial families of subsets with decidable and undecidable domino problem.


  • Domino Problem
  • Self-similar Substitution
  • Forbidden Patterns
  • Weak Grid
  • Strong Grid

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We would like to thank the reviewers for their helpful remarks. This work was partially supported by the ANR project QuasiCool (ANR-12-JS02-011-01)

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Correspondence to Sebastián Barbieri .

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© 2016 Springer International Publishing Switzerland

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Barbieri, S., Sablik, M. (2016). The Domino Problem for Self-similar Structures. In: Beckmann, A., Bienvenu, L., Jonoska, N. (eds) Pursuit of the Universal. CiE 2016. Lecture Notes in Computer Science(), vol 9709. Springer, Cham.

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40188-1

  • Online ISBN: 978-3-319-40189-8

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