A1 Journal article – refereed

On the domino problem of the Baumslag-Solitar groups




List of Authors: Aubrun Nathalie, Kari Jarkko

Publisher: Elsevier B.V.

Publication year: 2021

Journal: Theoretical Computer Science

Journal name in source: Theoretical Computer Science

ISSN: 0304-3975

eISSN: 1879-2294

DOI: http://dx.doi.org/10.1016/j.tcs.2021.09.002

URL: https://www.sciencedirect.com/science/article/pii/S030439752100517X


Abstract

In [1] we construct aperiodic tile sets on the Baumslag-Solitar groups BS(m, n). Aperiodicity plays a central role in the undecidability of the classical domino problem on Z2, and analogously to this we state as a corollary of the main construction that the Domino problem is undecidable on all Baumslag-Solitar groups. In the present work we elaborate on the claim and provide a full proof of this fact. We also provide details of another result reported in [1]: there are tiles that tile the Baumslag-Solitar group BS(m, n)but none of the valid tilings is recursive. The proofs are based on simulating piecewise affine functions by tiles on BS(m, n).


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Last updated on 2021-18-10 at 11:51