A generalized approach to formal languages

摘要

A generalization of ranked alphabets, many-sorted alphabets, is studied. The concepts of finite automaton, regular, recognizable, equational, and context free languages are generalized to sets over these new alphabets. It is shown that the derivation trees of a context free set are always characterized by some recognizable set over a related many-sorted alphabet. Previous theory is drawn as a special case of these results and new results are advanced. A number of suggestions about language theory are made.