Decidability and Universality of Quasiminimal Subshifts
Abstract
We introduce the quasiminimal subshifts, subshifts having only finitely many subsystems. With $\mathbb{N}$-actions, their theory essentially reduces to the theory of minimal systems, but with $\mathbb{Z}$-actions, the class is much larger. We show many examples of such subshifts, and in particular construct a universal system with only a single proper subsystem, refuting a conjecture of [Delvenne, Kůrka, Blondel, '05].
- Publication:
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arXiv e-prints
- Pub Date:
- November 2014
- DOI:
- 10.48550/arXiv.1411.6644
- arXiv:
- arXiv:1411.6644
- Bibcode:
- 2014arXiv1411.6644S
- Keywords:
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- Mathematics - Dynamical Systems;
- Computer Science - Formal Languages and Automata Theory
- E-Print:
- 40 pages, 1 figure, submitted to JCSS