Construction of pure grammars
A construction is described assigning a pure grammar G(mrn) to any language and to any integers 0 less than or equal to m less than or equal to r less than or equal to n. This construction has the following property: If the sequence (G(mrn))(ngreater than or equal tor) has a limit G(mr) for any r greater than or equal to m and if the sequence (G(mr))(rgreater than or equal tom) has a limit, then the given language is generated by a pure grammar. By a limit of a sequence (a(k))(kgreater than or equal tok0) we understand a member ak, of the sequence such that k(1) greater than or equal to k(0) and a(k) = ak(1) for any k greater than or equal to k(i).
pure grammar generalized pure grammar relation of domination reducing operator