Algorithmic randomness uses the tools of computability theory to analyze the question, "When is an infinite binary sequence random?".  Several different definitions of a random sequence are studied, with the most common being Martin-Löf randomness.

Randomness has a rich interaction with the Turing degrees of more classical computability theory, in particular with the c.e. degrees and the PA degrees. For example, if a random cannot compute \(0'\) (or equivalently, cannot compute a PA degree), then every c.e. set which it can compute is \(K\)-trivial, which means that randomness considers it useless as an oracle; despite being non-computable, it has no derandomization power. The covering problem asks if this can be reversed; is every \(K\)-trivial computable from a random that does not compute \(0'\)?

I will review the appropriate definitions and discuss the covering problem and similar questions. I will also discuss the proof of the covering problem, which touches on the interaction of algorithmic randomness and effective analysis.