When Stars Control a Grammar's Work

TL;DR

This paper investigates star-structured graph-controlled insertion-deletion systems, demonstrating their computational power when the control graph is restricted to a star shape with a central master component.

Contribution

It introduces a star-structured restriction to GCID systems and proves their computational completeness under certain complexity measures.

Findings

Star-structured GCID systems are computationally complete.

The central component acts as a master controlling the process.

Restrictions on the control graph shape affect computational power.

Abstract

Graph-controlled insertion-deletion (GCID) systems are regulated extensions of insertion-deletion systems. Such a system has several components and each component contains some insertion-deletion rules. The 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. The language of the system is the set of all terminal strings collected in the final component. We impose the restriction in the structure of the underlying graph to be a star structure where there is a central, control component which acts like a master and transmits a string (after applying one of its rules) to one of the components specified in the (applied) rule. A component which receives the string can process the obtained string with any applicable rule available in it and sends back the resultant string only to the center component. With this restriction, we obtain computational completeness for some descriptional complexity measures