A special class of stationary one-dependent two-valued stochastic processes is defined. We associate to each member of this class two parameter values, whereby different members receive different parameter values. For any given values of the parameters, we show how to determine whether: 1. a process exists having the given parameter values, and if so, 2. this process can be obtained as a two-block factor from an independent process. This determines a two-parameter subfamily of the class of stationary one-dependent two-valued stochastic processes which are not two-block factors of independent processes.
Jon Aaronson. David Gilat. Michael Keane. Vincent de Valk. "An Algebraic Construction of a Class of One-Dependent Processes." Ann. Probab. 17 (1) 128 - 143, January, 1989. https://doi.org/10.1214/aop/1176991499