All reports by Author David Doty:

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TR10-195
| 13th November 2010
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Ho-Lin Chen, David Doty, Shinnosuke Seki, David Soloveichik#### Parallelism, Program Size, Time, and Temperature in Self-Assembly

Revisions: 1

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TR10-131
| 9th July 2010
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Nathaniel Bryans, Ehsan Chiniforooshan, David Doty, Lila Kari, Shinnosuke Seki#### The Power of Nondeterminism in Self-Assembly

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TR06-080
| 16th June 2006
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David Doty#### Dimension Extractors

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TR06-038
| 10th February 2006
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David Doty, Jack H. Lutz, Satyadev Nandakumar#### Finite-State Dimension and Real Arithmetic

Ho-Lin Chen, David Doty, Shinnosuke Seki, David Soloveichik

We settle a number of questions in variants of Winfree's abstract Tile Assembly Model (aTAM), a model of molecular algorithmic self-assembly. In the "hierarchical" aTAM, two assemblies, both consisting of multiple tiles, are allowed to aggregate together, whereas in the "seeded" aTAM, tiles attach one at a time to a ... more >>>

Nathaniel Bryans, Ehsan Chiniforooshan, David Doty, Lila Kari, Shinnosuke Seki

We investigate the role of nondeterminism in Winfree's abstract Tile Assembly Model (aTAM), which was conceived to model artificial molecular self-assembling systems constructed from DNA. Designing tile systems that assemble shapes, due to the algorithmic richness of the aTAM, is a form of sophisticated "molecular programming". Of particular practical importance ... more >>>

David Doty

A dimension extractor is an algorithm designed to increase the effective dimension -- i.e., the computational information density -- of an infinite sequence. A constructive dimension extractor is exhibited by showing that every sequence of positive constructive dimension is Turing equivalent to a sequence of constructive strong dimension arbitrarily ... more >>>

David Doty, Jack H. Lutz, Satyadev Nandakumar

We use entropy rates and Schur concavity to prove that, for every integer k >= 2, every nonzero rational number q, and every real number alpha, the base-k expansions of alpha, q+alpha, and q*alpha all have the same finite-state dimension and the same finite-state strong dimension. This extends, and gives ... more >>>