Further remarks on DNA overlap assembly

The operation of overlap assembly was defined by Csuhaj-Varjú, Petre, and Vaszil as a formal model of the linear self-assembly of DNA strands: The overlap assembly of two strings, xy and yz, which share an “overlap” y, results in the string xyz. This paper continues the exploration of the properties of the overlap assembly operation by investigating closure of various language classes under iterated overlap assembly, and the decidability of the completeness of a language. It also investigates the problem of deciding whether a given string is terminal with respect to a language, and the problem of deciding if a given language can be generated by an overlap assembly operation of two given others.