Bonding Grammars
Tikhon Pshenitsyn
TL;DR
Bonding grammars address modeling DNA computation with graphs by replacing fusion with a bonding operation that merges two hyperedges into one with label $A \otimes B$, enabling a biologically grounded base-pair interpretation. The work formalizes BGs as $BG=(Z,N,T,\otimes)$ and analyzes their expressiveness relative to hyperedge replacement grammars, showing they can generate languages not captured by hyperedge replacement grammars while also naturally simulating regular sticker systems. It proves the bonding grammatical membership problem is in NP and, in fact, NP-complete, with NP-hardness established via reductions such as 5Conn-PiT; it also demonstrates that BGs can produce languages with unbounded treewidth, indicating a distinct expressive power from hyperedge replacement grammars. The paper positions bonding grammars as a computationally practical and biologically faithful extension of graph grammars for DNA computing and outlines future directions comparing them to fusion grammars and exploring extensions.
Abstract
We introduce bonding grammars, a graph grammar formalism developed to model DNA computation by means of graph transformations. It is a modification of fusion grammars introduced by Kreowski, Kuske and Lye in 2017. Bonding is a graph transformation that consists of merging two hyperedges into a single larger one. We show why bonding models interaction between DNA molecules better than fusion. Then, we investigate formal properties of this formalism. Firstly, we study the relation between bonding grammars and hyperedge replacement grammars proving that each of these kinds of grammars generates a language the other one cannot generate. Secondly, we prove that bonding grammars naturally generalise regular sticker systems. Finally, we prove that the membership problem for bonding grammars is NP-complete and, moreover, that some bonding grammar generates an NP-complete set.