Self-assembly of strings and languages

Further remarks on DNA overlap assembly

“…Therefore, the (positive) closure results for the iterated superposition, obtained in [22,31], also hold for the iterated overlap assembly. Indeed, the same results were independently obtained in [1], in its study of closure properties of iterated overlap assembly:…”

“…Formally, the overlap assembly between uv and θ(w)θ(v) is uvw. Assuming that all involved DNA strands are initially double-stranded, that is, whenever the strand x is available, its Watson-Crick complement θ(x) is also available, one can further simplify this model and, given two words x, y over an alphabet Σ, define the overlap assembly of x with y, [1], as:…”

“…The word and language operation overlap assembly was first introduced by Csuhaj-Varju, Petre, and Vaszil -under the name (self-)assembly -in [1], and later studied in [2], as a formal model of the linear self-assembly of DNA strands. Formally, the overlap assembly is a binary operation which, when applied to two input strings xy and yz (where y is their nonempty overlap), produces the output xyz.…”

“…Overlap assembly can also be viewed as modelling a special case of an experimental procedure called cross-pairing PCR, introduced in [14] and studied in, e.g., [15,16,17,18]. This paper is a continuation of the theoretical analysis of overlap assembly as a formal language operation, that was started in [1] and [2]. In [1], the authors proposed a formal language operation called "self-assembly", inspired by the linear self-assembly of DNA single strands via Watson-Crick complementarity.…”

“…This paper is a continuation of the theoretical analysis of overlap assembly as a formal language operation, that was started in [1] and [2]. In [1], the authors proposed a formal language operation called "self-assembly", inspired by the linear self-assembly of DNA single strands via Watson-Crick complementarity. The authors obtained closure properties of various language classes under iterated overlap assembly, and studied the question of whether or not a given language can be generated through assembly and, if so, what is the minimal generator.…”