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Computable randomness is a central notion in algorithmic randomness, which is usually defined using
"betting strategies" for betting on the digits of an infinite sequence. The notion can be
strengthened by allowing strategies that bet on the digits in a non-monotonic order, e.g.
in an order given by a computable permutation or injection.
In this seminar, I will first
prove that for total betting strategies, permutation betting strategies are not more powerful
than ordinary betting strategies; i.e. total permutation randomness is equivalent with computable
randomness. However, injection betting strategies are more powerful, which I will show by giving
my own construction of a partial computable random sequence that is not total injection random.
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