Universality by Finite H Systems

Abstract

As we have seen in the previous chapter, extended H systems with finite sets of axioms and splicing rules are able to generate only regular languages. As we are looking for generative (computability) models having the power of Turing machines, we have to consider features that can increase the power of H systems. This has been successfully done for Chomsky grammars and other generative mechanisms in the regulated rewriting area and the grammar systems area. Following suggestions from these areas, as well as suggestions offered by the proof of the Basic Universality Lemma (Lemma 7.16), in this chapter we shall consider a series of controlled H systems with finite components which characterize the recursively enumerable languages, hence are computationally complete. From the proofs, we shall also obtain universal computing devices, hence models of “programmable DNA computers based on splicing”.