On the overlap assembly of strings and languages

Abstract

This paper investigates properties of the binary string and language operation overlap assembly which was defined by Csuhaj-Varju, 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. The study of overlap assembly as a formal language operation is part of ongoing efforts to provide a formal framework and rigorous treatment of DNA-based information and DNA-based computation. Other studies along these lines include theoretical explorations of splicing systems, insertion/deletion systems, substitution, hairpin extension, hairpin reduction, superposition, overlapping catenation, conditional concatenation, contextual intra- and intermolecular recombinations, template guided recombination, as well as directed extension by PCR. In this context, we investigate overlap assembly and its properties: closure properties of basic language families under this operation, decision problems, as well as the possible use of iterated overlap assembly to generate combinatorial DNA libraries.