Extend bonding grammars with additional DNA computation operations

Develop extensions of bonding grammars that incorporate graph transformation rules modeling DNA computing operations other than the bonding operation, thereby enabling the simulation of additional DNA computing processes within the bonding grammar framework.

Background

The paper introduces bonding grammars as a graph grammar formalism tailored to model DNA computation, where bonding merges two hyperedges (representing complementary nucleobases) into a single terminal hyperedge (representing a base pair). It demonstrates key properties of bonding grammars, including their relationship with hyperedge replacement grammars, an embedding of regular sticker systems, and NP-completeness of the membership problem.

The author concludes by pointing to further directions: while bonding captures base-pair formation, DNA computing involves additional operations beyond bonding. Extending bonding grammars to include such operations via graph transformations would broaden the formalism’s applicability and is explicitly stated as an open problem.

References

Studying extensions of bonding grammars with such operations is an open problem.

— Bonding Grammars  (2401.14377 - Pshenitsyn, 2024) in Conclusion (final paragraph before Credits)

In particular, an interesting direction for future work is to investigate how activity, such as that generated by polymerases, and DNA supercoiling would couple to our protocols, since energy-consuming enzymes and torsional stress could provide additional non-equilibrium levers on the mobility of the gel and rewriting of entanglements.

— Design Principles for Programmable Topological Soft Networks  (2610.08298 - Bonato et al., 6 Oct 2026) in Conclusion