Computational Completeness of Path-Structured Graph-Controlled Insertion-Deletion Systems

Abstract

A graph-controlled insertion-deletion (GCID) system is a regulated extension of an insertion-deletion system. It has several components and each component contains some insertion-deletion rules. These components are the vertices of a directed control graph. A rule is applied to a string in a component and the resultant string is moved to the target component specified in the rule, describing the arcs of the control graph. We investigate which combinations of size parameters (the maximum number of components, the maximal length of the insertion string, the maximal length of the left context for insertion, the maximal length of the right context for insertion; a similar three restrictions with respect to deletion) are sufficient to maintain the computational completeness of such restricted systems with the additional restriction that the control graph is a path, thus, these results also hold for ins-del P systems.