Splicing on tree-like structures

In this paper, we provide a method to increase the power of splicing systems. We introduce the splicing systems on trees to be built as partially annealed single strands, which is a quite similar notion and a natural extension of splicing systems on strings. Trees are a common and useful data structure in computer science and have a biological counterpart such as molecular sequences with secondary structures, which are typical structures in RNA sequences. Splicing on trees involves (1) complete subtrees as axioms, (2) restriction operated on the annealed subsequences, (3) rules to substitute a complete subtree with another. We show that splicing systems on trees with finite sets of axioms and finite sets of rules can generate the class of context-free languages without the need of imposing multiplicity constraints.