Zero-error capacity for models with memory and the enlightened dictator channel

Summary form only given. We present a general class of "combinatorial" 0-error capacity problems with the "memory" covering known and many new cases. This class can be incorporated into a model of channels with memory. W analyse a seemingly basic channel in this class, which we call the "dictator channel". Clearly, a dictator always follows his own opinion. However, we speak of an enlightened dictator, if he responds to the unanimous vote of the people against his opinion to the degree, in this case he reaches a decision by coin tossing.