I am broadly interested in the design and analysis of algorithms, especially when it involves randomness and applications to large data sets.Previously, I graduated from Caltech with a degree in computer science in 2016.
My CV is available.
Nicholas Schiefer and Erik Winfree, “Time Complexity of Computation and Construction in the Chemical Reaction Network-Controlled Tile Assembly Model”, 22nd International Conference on DNA Computing and Molecular Programming (DNA22), 2016.
In isolation, chemical reaction networks and tile-based self-assembly are well-studied models of chemical computation. Previously, we introduced the chemical reaction network-controlled tile assembly model (CRN-TAM), in which a stochastic chemical reaction network can act as a non-local control and signalling system for tile-based assembly, and showed that the CRN-TAM can perform several tasks related to the simulation of Turing machines and construction of algorithmic shapes with lower space or program complexity than in either of its parent models. Here, we introduce a kinetic variant of the CRN-TAM and investigate the time complexity of computation and construction. We analyze the time complexity of decision problems in the CRN-TAM, and show that decidable languages can be decided as efficiently by CRN-TAM programs as by Turing machines. We also give a lower bound for the space-time complexity of CRN-TAM computation that rules out efficient parallel stack machines. We provide efficient parallel implementations of non-deterministic computations, showing among other things that CRN-TAM programs can decide languages in NTIME ∩ coNTIME(f(n)) in O(f(n) + n + log c) time with (1 - exp (-c)) probability, using volume exponential in n. Lastly, we provide basic mechanisms for parallel computations that share information and illustrate the limits of parallel computation in the CRN-TAM.
Nicholas Schiefer and Erik Winfree, “Universal Computation and Optimal Construction in the Chemical Reaction Network-Controlled Tile Assembly Model”, 21st International Conference on DNA Computing and Molecular Programming (DNA21), 2015, Lecture Notes in Computer Science vol. 9211, pp. 34–54.
Tile-based self-assembly and chemical reaction networks provide two well-studied models of scalable DNA-based computation. Although tile self-assembly provides a powerful framework for describing Turing-universal self-assembling systems, assembly logic in tile self-assembly is localized, so that only the nearby environment can affect the process of self-assembly. We introduce a new model of tile-based self-assembly in which a well-mixed chemical reaction network interacts with self-assembling tiles to exert non-local control on the self-assembly process. Through simulation of multi-stack machines, we demonstrate that this new model is efficiently Turing-universal, even when restricted to unbounded space in only one spatial dimension. Using a natural notion of program complexity, we also show that this new model can produce many complex shapes with programs of lower complexity. Most notably, we show that arbitrary connected shapes can be produced by a program with complexity bounded by the Kolmogorov complexity of the shape, without the large scale factor that is required for the analogous result in the abstract tile assembly model. These results suggest that controlled self-assembly provides additional algorithmic power over tile-only self-assembly, and that non-local control enhances our ability to perform computation and algorithmically self-assemble structures from small input programs.
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