Adding Matrix Control: Insertion-Deletion Systems with Substitutions III

Abstract

Insertion-deletion systems have been introduced as a formalism to model operations that find their counterparts in ideas of bio-computing, more specifically, when using DNA or RNA strings and biological mechanisms that work on these strings. So-called matrix control has been introduced to insertion-deletion systems in order to enable writing short program fragments. We discuss substitutions as a further type of operation, added to matrix insertion-deletion systems. For such systems, we additionally discuss the effect of appearance checking. This way, we obtain new characterizations of the family of context-sensitive and the family of recursively enumerable languages. Not much context is needed for systems with appearance checking to reach computational completeness. This also suggests that bio-computers may run rather traditionally written programs, as our simulations also show how Turing machines, like any other computational device, can be simulated by certain matrix insertion-deletion-substitution systems.