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A simple bound is that we could use a program generating $x$, a starting index $1 \leq i \leq n$ and length $m$ to get a program generating any choice of $v$, and thus $C(v)$ is bounded as $$\forall v: k \leq C(v) \leq C(x) + \log(n) + \log(m) + c,$$ where $c$ is some constant overhead independent from $x,v$ that represents the steps necessary to take a ...


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