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- David Doty, Jack H. Lutz, Matthew J. Patitz, Robert T. Schweller, Scott M. Summers, Damien Woods
- 2012 IEEE 53rd Annual Symposium on Foundations of…
- 2012

We prove that the abstract Tile Assembly Model (aTAM) of nanoscale self-assembly is intrinsically universal. This means that there is a single tile assembly system U that, with proper initialization, simulates any tile assembly system T. The simulation is "intrinsic" in the sense that the self-assembly process carried out by U is exactly that carried out by… (More)

- Damien Woods
- Encyclopedia of Algorithms
- 2010

We show that the Tile Assembly Model exhibits a strong notion of universality where the goal is to give a single tile assembly system that simulates the behavior of any other tile assembly system. We give a tile assembly system that is capable of simulating a very wide class of tile systems, including itself. Specifically, we give a tile set that simulates… (More)

- Damien Woods, Ho-Lin Chen, Scott Goodfriend, Nadine Dabby, Erik Winfree, Peng Yin
- ITCS
- 2013

We describe a computational model for studying the complexity of self-assembled structures with active molecular components. Our model captures notions of growth and movement ubiquitous in biological systems. The model is inspired by biology's fantastic ability to assemble biomolecules that form systems with complicated structure and dynamics, from… (More)

- Turlough Neary, Damien Woods
- ICALP
- 2006

We show that the problem of predicting t steps of the 1D cellular automaton Rule 110 is P-complete. The result is found by showing that Rule 110 simulates deterministic Turing machines in polynomial time. As a corollary we find that the small universal Turing machines of Mathew Cook run in polynomial time, this is an exponential improvement on their… (More)

- Turlough Neary, Damien Woods
- MCU
- 2007

We present small polynomial time universal Turing machines with state-symbol pairs of (5, 5), (6, 4), (9, 3) and (18, 2). These machines simulate our new variant of tag system, the bi-tag system and are the smallest known universal Turing machines with 5, 4, 3 and 2-symbols respectively. Our 5-symbol machine uses the same number of instructions (22) as the… (More)

- Damien Woods, Turlough Neary
- 2006 47th Annual IEEE Symposium on Foundations of…
- 2006

We show that 2-tag systems efficiently simulate Turing machines. As a corollary we find that the small universal Turing machines of Rogozhin, Minsky and others simulate Turing machines in polynomial time. This is an exponential improvement on the previously known simulation time overhead and improves a forty year old result in the area of small universal… (More)

- Damien Woods, Turlough Neary
- CiE
- 2007

- Turlough Neary, Damien Woods
- FCT
- 2009

We give small universal Turing machines with state-symbol pairs of (6, 2), (3, 3) and (2, 4). These machines are weakly universal, which means that they have an infinitely repeated word to the left of their input and another to the right. They simulate Rule 110 and are currently the smallest known weakly universal Turing machines. Despite their small size… (More)

- Damien Woods, Thomas J. Naughton
- Applied Mathematics and Computation
- 2009

In this survey we consider optical computers that encode data using images and compute by transforming such images. We give an overview of a number of such optical computing archi-tectures, including descriptions of the type of hardware commonly used in optical computing, as well as some of the computational efficiencies of optical devices. We go on to… (More)

We prove a negative result on the power of a model of algorithmic self-assembly for which it has been notoriously difficult to find general techniques and results. Specifically, we prove that Winfree's abstract Tile Assembly Model, when restricted to use noncooperative tile binding, is not intrinsically universal. This stands in stark contrast to the recent… (More)