Computational power of insertion–deletion (P) systems with rules of size two

Matrix insertion–deletion systems

“…In the case of first two systems matrices of size 3 are used, while in the case of the last two systems binary matrices are sufficient. Since a matrix control is a particular case of a graph control (having an input/output node and series of linear paths starting and ending in this node), we obtain [14] that matrix insertion-deletion systems having rules of size (2, 0, 0; 2, 0, 0) are not computationally complete.…”

“…For all the variants of insertion and deletion rules considered in this section, we know that the basic variants without using matrix control cannot achieve computational completeness (see [14], [17]). The computational completeness results from this section are based on simulations of derivations of a grammar in the special Geffert normal form.…”

Graph-Controlled Insertion-Deletion Systems

“…This correspond to systems of size (1, 1, 0; 1, 1, 0), (1, 1, 0; 1, 0, 1), (1, 1, 0; 2, 0, 0), and (2, 0, 0; 1, 1, 0), where the first three numbers represent the maximal size of the inserted string and the maximal size of the left and right contexts, while the last three numbers represent the same information, but for deletion rules. It is known that such systems are not computationally complete [13], while the corresponding P systems variants are computationally complete, which results are achieved with five components. In this article we give a simpler definition of the concept of graph-controlled insertion-deletion systems and we show that computational completeness can already be achieved by using a control graph with only four nodes (components).…”

Outfix-guided insertion

“…Contextual insertion-deletion systems in the study of molecular computing have been used e.g. by Daley et al [4], Enaganti et al [7], Krassovitskiy et al [17] and Takahara and Yokomori [24]. Further theoretical studies on the computational power of insertion-deletion systems were done e.g.…”