2014/05/02 by Moya Chen, Chen, Moya, Doris Xin +3
Biochemistry, Genetics and Molecular Biology · Computer Science · #Advanced biosensing and bioanalysis techniques #Cellular Automata and Applications #Computational Complexity (cs.CC) #DNA and Biological Computing #Data Structures and Algorithms (cs.DS) #Emerging Technologies (cs.ET) #FOS: Computer and information sciences #Robotics (cs.RO) #cs.CC #cs.DS #cs.ET #cs.RO
paper · pdf · doi:10.48550/arxiv.1405.0527
Journal version to appear in Natural Computing. Earlier conference version appeared at DNA19
openalex publication_date 2014/05/02 · arxiv created 2014/09/05 · arxiv updated 2014/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the computational complexity of the recently proposed nubot model of molecular-scale self-assembly. The model generalises asynchronous cellular automata to have non-local movement where large assemblies of molecules can be pushed and pulled around, analogous to millions of molecular motors in animal muscle effecting the rapid movement of macroscale arms and legs. We show that the nubot model is capable of simulating Boolean circuits of polylogarithmic depth and polynomial size, in only polylogarithmic expected time. In computational complexity terms, we show that any problem from the complexity class NC is solvable in polylogarithmic expected time and polynomial workspace using nubots. Along the way, we give fast parallel nubot algorithms for a number of problems including line growth, sorting, Boolean matrix multiplication and space-bounded Turing machine simulation, all using a constant number of nubot states (monomer types). Circuit depth is a well-studied notion of parallel time, and our result implies that the nubot model is a highly parallel model of computation in a formal sense. Asynchronous cellular automata are not capable of this parallelism, and our result shows that adding a rigid-body movement primitive to such a model, to get the nubot model, drastically increases parallel processing abilities.