We prove that every computably enumerable (c.e.) random real is provable in Peano Arithmetic (PA) to be c.e. random. A major step in the proof is to show that the theorem stating ...
The computable Lipschitz reducibility was introduced by Downey, Hirschfeldt and LaForte under the name of strong weak truthtable reducibility [6]. This reducibility measures both t...
We define a class of “algebraic” random matrix channels for which one can generically compute the limiting Shannon transform using numerical techniques and often enumerate th...
The strong weak truth table reducibility was suggested by Downey, Hirschfeldt, and LaForte as a measure of relative randomness, alternative to the Solovay reducibility. It also occ...
We say that A LR B if every B-random number is A-random. Intuitively this means that if oracle A can identify some patterns on some real , oracle B can also find patterns on . In o...
George Barmpalias, Andrew E. M. Lewis, Mariya Ivan...