On test sets for checking morphism equivalence on languages with fair distribution of letters

AbstractA test set for a language L is a finite subset T of L with the property that each pair of morphisms that agrees on T also agrees on L. Some results concerning test sets for languages with fair distribution of letters are presented. The first result is that every D0L language with fair distribution of letters has a test set. The second result shows that every language L with fair distribution has a test set relative to morphisms g, h which have bounded balance on L. These results are generalizations of results of Culik II and Karhumäki (1983)