Cellular automata between sofic tree shifts
نویسندگان
چکیده
منابع مشابه
Cellular automata between sofic tree shifts
We study the sofic tree shifts of A ∗ , where Σ∗ is a regular rooted tree of finite rank. In particular, we give their characterization in terms of unrestricted Rabin automata. We show that if X ⊂ A ∗ is a sofic tree shift, then the configurations in X whose orbit under the shift action is finite are dense in X , and, as a consequence of this, we deduce that every injective cellular automata τ ...
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We investigate the computational properties of cellular automata on countable (equivalently, zero entropy) sofic shifts with an emphasis on nilpotency, periodicity, and asymptotic behavior. As a tool for proving decidability results, we prove the Starfleet Lemma, which is of independent interest. We present computational results including the decidability of nilpotency and periodicity, the unde...
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Let M = Z be a D-dimensional lattice, and let (A,+) be an abelian group. AM is then a compact abelian group under componentwise addition. A continuous function : AM −→ AM is called a linear cellular automaton if there is a finite subset F ⊂ M and non-zero coefficients φf ∈ Z so that, for any a ∈ AM, (a) = ∑ f∈F φf · σ f(a). Suppose that μ is a probability measure onAM whose support is a subshif...
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Let V be a finite-dimensional vector space over a field K and let G be a sofic group. We show that every injective linear cellular automaton τ : V G → V G is surjective. As an application, we obtain a new proof of the stable finiteness of group rings of sofic groups, a result previously established by G. Elek and A. Szabó using different methods.
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We introduce the notion of sofic tree-shifts which corresponds to symbolic dynamical systems of infinite trees accepted by finite tree automata. We show that, contrary to shifts of infinite sequences, there is no unique minimal deterministic irreducible tree automaton accepting an irreducible sofic tree-shift, but that there is a unique synchronized one, called the Shannon cover of the tree-shi...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2013
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2013.07.007