On Characterizing Recursively Enumerable Languages by Insertion Grammars

摘要

Insertion grammars have been introduced in [1] and their computational power has been studied in several places. In [7] it is proved that insertion grammars with weight at least 7 can characterize recursively enumerable languages (modulo a weak coding and an inverse morphism), and the question was formulated whether or not this result can be improved. In this paper, we come up with a positive answer to this question, by decreasing the weight of the insertion grammar used to 5. We also give a characterization of recursively enumerable languages in terms of right quotients of insertion languages.