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Parallel Computation Using Active Self-assembly

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DNA Computing and Molecular Programming (DNA 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8141))

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Abstract

We study the computational complexity of the recently proposed nubots model of molecular-scale self-assembly. The model generalizes asynchronous cellular automaton to have non-local movement where large assemblies of molecules can be moved around, analogous to millions of molecular motors in animal muscle effecting the rapid movement of large arms and legs. We show that nubots is capable of simulating Boolean circuits of polylogarithmic depth and polynomial size, in only polylogarithmic expected time. In computational complexity terms, any problem from the complexity class NC is solved in polylogarithmic expected time on nubots that use a polynomial amount of workspace. Along the way, we give fast parallel 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 nubots is a highly parallel model of computation in a formal sense. Thus, adding a movement primitive to an asynchronous non-deterministic cellular automation, as in nubots, drastically increases its parallel processing abilities.

Supported by National Science Foundation grants CCF-1219274, 0832824 (The Molecular Programming Project), and CCF-1162589. mpchen@caltech.edu, doris.s.xin@gmail.com, woods@caltech.edu. A full version of this paper will appear on the arXiv.

The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: 10.1007/978-3-319-01928-4_15

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Authors and Affiliations

  1. California Institute of Technology, Pasadena, CA, 91125, USA

    Moya Chen, Doris Xin & Damien Woods

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  1. Moya Chen
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  2. Doris Xin
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  1. Center for Systems and Synthetic Biology, University of California, 1700 4th Street, San Francisco, 94158, CA, USA

    David Soloveichik

  2. Materials Science and Engineering Department, Boise State University, 1910 University Drive, 83725, Boise, ID, USA

    Bernard Yurke

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Chen, M., Xin, D., Woods, D. (2013). Parallel Computation Using Active Self-assembly. In: Soloveichik, D., Yurke, B. (eds) DNA Computing and Molecular Programming. DNA 2013. Lecture Notes in Computer Science, vol 8141. Springer, Cham. https://doi.org/10.1007/978-3-319-01928-4_2

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  • DOI: https://doi.org/10.1007/978-3-319-01928-4_2

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