An alternative definition of splicing

In this paper, we propose a new definition of the language generated by a splicing system, motivated by both biochemical and mathematical considerations. The main feature of the new definition is that by applying a splicing rule, we not only create new strings, but also allow for the removal of the strings entering the rule. This behaviour seems to correspond better to biochemical reality and is in fact used as a tool in several experimental DNA computations. We show that using this new definition, finite extended H$H$ systems can generate all recursively enumerable languages. Even a weaker version of these H$H$ systems, defined using the new notion of delay, is shown to be strictly more powerful than H$H$ systems defined in the traditional way.