Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Martin-L\"of reducibility and cost functions   Martin-L\"of (ML)-reducibility compares $K$-trivial sets by examining the
Martin-L\"of random sequences that compute them. We show that every $K$-trivial
set is computable from a c.e.\ set of the same ML-degree. We investigate the
interplay between ML-reducibility and cost functions, which are used to both
measure the number of changes in a computable approximation, and the type of
null sets used to capture ML-random sequences. We show that for every cost
function there is a c.e.\ set ML-above the sets obeying it (called an
ML-complete set for the cost function). We characterise the $K$-trivial sets
computable from a fragment of the left-c.e.\ random real~$\Omega$. This leads
to a new characterisation of strong jump-traceability.

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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an