DNA computing based on splicing: universality results

The paper extends some of the most recently obtained results on the computational universality of specific variants of H systems (e.g. with regular sets of rules) and proves that we can construct universal computers based on various types of H systems with a finite set of splicing rules as well as a finite set of axioms, i.e. we show the theoretical possibility to design programmable universal DNA computers based on the splicing operation. For H systems working in the multiset style (where the numbers of copies of all available strings are counted) we elaborate how a Turing machine computing a partial recursive function can be simulated by an equivalent H system computing the same function; in that way, from a universal Turning machine we obtain a universal H system. Considering H systems as language generating devices we have to add various simple control mechanisms (checking the presence/absence of certain symbols in the spliced strings) to systems with a finite set of splicing rules as well as with a finite set of axioms in order to obtain the full computational power, i.e. to get a characterization of the family of recursively enumerable languages. We also introduce test tube systems, where several H systems work in parallel in their tubes and from time to time the contents of each tube are redistributed to all tubes according to certain separation conditions. By the construction of universal test tube systems we show that also such systems could serve as the theoretical basis for the development of biological (DNA) computers.