  One of the cornerstones of the distributed complexity theory is the
derandomization result by Chang, Kopelowitz, and Pettie [FOCS 2016]: any
randomized LOCAL algorithm that solves a locally checkable labeling problem
(LCL) can be derandomized with at most exponential overhead. The original proof
assumes that the number of random bits is bounded by some function of the input
size. We give a new, simple proof that does not make any such assumptions-it
holds even if the randomized algorithm uses infinitely many bits. While at it,
we also broaden the scope of the result so that it is directly applicable far
beyond LCL problems.
