We study the computational power of pure insertion grammars. We show that pure insertion grammars of weight 3 can characterize all recursively enumerable languages. This is achieved by either applying an inverse morphism and a weak coding, or a left (right) quotient with a regular language. We also study an application in DNA computing and improve some known results concerning the power of insertion-deletion DNA systems. © 2008 Elsevier Ltd. All rights reserved.
Kari, L., & Sosík, P. (2008). On the weight of universal insertion grammars. Theoretical Computer Science, 396(1–3), 264–270. https://doi.org/10.1016/j.tcs.2008.01.037