Asymptotic randomization of sofic shifts by linear cellular automata
نویسندگان
چکیده
منابع مشابه
Asymptotic randomization of sofic shifts by linear cellular automata
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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If A = Z/2, then A Z is a compact abelian group. A linear cellular automaton is a shift-commuting endomorphism Φ of A. If μ is a probability measure on A, then Φ asymptotically randomizes μ if Φjμ converges to the Haar measure as j→∞, for j in a subset of Cesàro density one. Via counterexamples, we show that nonzero entropy of μ is neither necessary nor sufficient for asymptotic randomization. ...
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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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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2006
ISSN: 0143-3857,1469-4417
DOI: 10.1017/s0143385706000228