Networks of Watson-Crick D0L systems with communication by substrings

Abstract

Watson-Crick D0L systems (WD0L systems) are augmented variants of D0L systems defined over a DNA-like alphabet, where each letter has a complementary letter and this relation is symmetric. WD0L systems operate under a control that is inspired by the well-known phenomenon of Watson-Crick complementarity of the double helix of DNA. Depending on a trigger, the standard D0L rewriting step is applied either to the string or to its complementary string. In this paper, we examine extended networks of standard Watson-Crick D0L systems (ENSWD0L systems) with a variant of incomplete communication. An NWD0L system is a finite set of WD0L systems defined over a common DNA-like alphabet and operating in a synchronized manner. After rewriting their own strings in the WD0L manner, they communicate copies of certain generated strings (the so-called good strings) to the other nodes. In some previous papers, it was shown that ENSWD0L systems are computationally complete, and their computational power does not change if the communicated string is a non-empty prefix (non-empty suffix) of the generated string. We strengthen the previous results, namely we show that ENSWD0L systems are computationally complete even if the communicated string is an arbitrary substring of the generated string.