On cardinality questions concerning automaton mappings
András Ádám, Miklós Laczkovich · Studia Scientiarum Mathematicarum Hungarica · 2003
Let F+(X) be the set of words of positive length over a finite setX. By an automaton mapping (over (X,Y)) we understand a mapping of F+(X) into a finite setYwhere |Y|?1). The family of all mappings over (X,Y) may be considered as an infinite automatonUhaving 2?states.Uhas at most 2^{2?} subautomata and at most 2?countable subautomata. We show that these bounds are actually attained.