2013/04/25 by Andrew Winslow, Winslow, Andrew · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · #Advanced biosensing and bioanalysis techniques #Computational Complexity (cs.CC) #Computational Geometry (cs.CG) #DNA and Biological Computing #FOS: Computer and information sciences #Modular Robots and Swarm Intelligence #cs.CC #cs.CG
paper · pdf · doi:10.48550/arxiv.1304.7038
34 pages, 23 figures. An abstract version has been accepted to DNA 19
openalex publication_date 2013/04/25 · arxiv created 2013/06/29 · arxiv updated 2013/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Previous work by Demaine et al. (2012) developed a strong connection between smallest context-free grammars and staged self-assembly systems for one-dimensional strings and assemblies. We extend this work to two-dimensional polyominoes and assemblies, comparing staged self-assembly systems to a natural generalization of context-free grammars we call polyomino context-free grammars (PCFGs). We achieve nearly optimal bounds on the largest ratios of the smallest PCFG and staged self-assembly system for a given polyomino with n cells. For the ratio of PCFGs over assembly systems, we show the smallest PCFG can be an Omega(n/(log(n))3)-factor larger than the smallest staged assembly system, even when restricted to square polyominoes. For the ratio of assembly systems over PCFGs, we show that the smallest staged assembly system is never more than a O(log(n))-factor larger than the smallest PCFG and is sometimes an Omega(log(n)/loglog(n))-factor larger.