  We show that a large class of stationary continuous-time regenerative
processes are finitarily isomorphic to one another. The key is showing that any
stationary renewal point process whose jump distribution is absolutely
continuous with exponential tails is finitarily isomorphic to a Poisson point
process. We further give simple necessary and sufficient conditions for a
renewal point process to be finitarily isomorphic to a Poisson point process.
This improves results and answers several questions of Soo and of Kosloff and
Soo.
