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PreprintCC BY-SA 4.0HAL

Pimp my fixpoint: sofic realization of multidimensional substitution-based shift spaces

  • Antonin Callard
  • Pierre Guillon
  • Léo Paviet Salomon
  • Pascal Vanier
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Abstract

In symbolic dynamics, the fixed-point construction from [DRS12] defines shift spaces of finite type whose configurations embed infinite hierarchies of tilings. This article provides a "black box" abstraction of this method phrased in terms of substitutions and S-adic limit spaces operating over sequences of increasingly large alphabets. By quantifying the amount of information computed by the substitutions at each level, and using a suitable parallel model of computation, we provide a simple positive criterion of multidimensional soficity that generalizes classical examples from the literature.

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Cite

BibTeXRIS
BibTeX
@misc{callard2026pimp,
  title = {{Pimp my fixpoint: sofic realization of multidimensional substitution-based shift spaces}},
  author = {Antonin Callard and Pierre Guillon and Léo Paviet Salomon and Pascal Vanier},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.28207},
  eprint = {2609.28207},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05761449v1},
  note = {CC BY-SA 4.0},
}
RIS
TY  - UNPB
TI  - Pimp my fixpoint: sofic realization of multidimensional substitution-based shift spaces
AU  - Antonin Callard
AU  - Pierre Guillon
AU  - Léo Paviet Salomon
AU  - Pascal Vanier
PY  - 2026
DA  - 2026/09/23
PB  - HAL
DO  - 10.48550/arxiv.2609.28207
UR  - https://hal.science/hal-05761449v1
AB  - In symbolic dynamics, the fixed-point construction from [DRS12] defines shift spaces of finite type whose configurations embed infinite hierarchies of tilings. This article provides a "black box" abstraction of this method phrased in terms of substitutions and S-adic limit spaces operating over sequences of increasingly large alphabets. By quantifying the amount of information computed by the substitutions at each level, and using a suitable parallel model of computation, we provide a simple positive criterion of multidimensional soficity that generalizes classical examples from the literature.
ER  -