1,997 research outputs found
On the Computational Power of DNA Annealing and Ligation
In [20] it was shown that the DNA primitives of Separate,
Merge, and Amplify were not sufficiently powerful to invert
functions defined by circuits in linear time. Dan Boneh et
al [4] show that the addition of a ligation primitive, Append, provides the missing power. The question becomes, "How powerful is ligation? Are Separate, Merge, and Amplify
necessary at all?" This paper proposes to informally explore
the power of annealing and ligation for DNA computation.
We conclude, in fact, that annealing and ligation alone are
theoretically capable of universal computation
Defect Particle Kinematics in One-Dimensional Cellular Automata
Let A^Z be the Cantor space of bi-infinite sequences in a finite alphabet A,
and let sigma be the shift map on A^Z. A `cellular automaton' is a continuous,
sigma-commuting self-map Phi of A^Z, and a `Phi-invariant subshift' is a
closed, (Phi,sigma)-invariant subset X of A^Z. Suppose x is a sequence in A^Z
which is X-admissible everywhere except for some small region we call a
`defect'. It has been empirically observed that such defects persist under
iteration of Phi, and often propagate like `particles'. We characterize the
motion of these particles, and show that it falls into several regimes, ranging
from simple deterministic motion, to generalized random walks, to complex
motion emulating Turing machines or pushdown automata. One consequence is that
some questions about defect behaviour are formally undecidable.Comment: 37 pages, 9 figures, 3 table
Upper Bound on the Products of Particle Interactions in Cellular Automata
Particle-like objects are observed to propagate and interact in many
spatially extended dynamical systems. For one of the simplest classes of such
systems, one-dimensional cellular automata, we establish a rigorous upper bound
on the number of distinct products that these interactions can generate. The
upper bound is controlled by the structural complexity of the interacting
particles---a quantity which is defined here and which measures the amount of
spatio-temporal information that a particle stores. Along the way we establish
a number of properties of domains and particles that follow from the
computational mechanics analysis of cellular automata; thereby elucidating why
that approach is of general utility. The upper bound is tested against several
relatively complex domain-particle cellular automata and found to be tight.Comment: 17 pages, 12 figures, 3 tables,
http://www.santafe.edu/projects/CompMech/papers/ub.html V2: References and
accompanying text modified, to comply with legal demands arising from
on-going intellectual property litigation among third parties. V3: Accepted
for publication in Physica D. References added and other small changes made
per referee suggestion
Fuzzy cellular model for on-line traffic simulation
This paper introduces a fuzzy cellular model of road traffic that was
intended for on-line applications in traffic control. The presented model uses
fuzzy sets theory to deal with uncertainty of both input data and simulation
results. Vehicles are modelled individually, thus various classes of them can
be taken into consideration. In the proposed approach, all parameters of
vehicles are described by means of fuzzy numbers. The model was implemented in
a simulation of vehicles queue discharge process. Changes of the queue length
were analysed in this experiment and compared to the results of NaSch cellular
automata model.Comment: The original publication is available at http://www.springerlink.co
DNA Computing by Self-Assembly
Information and algorithms appear to be central to biological organization
and processes, from the storage and reproduction of genetic information to
the control of developmental processes to the sophisticated computations
performed by the nervous system. Much as human technology uses electronic
microprocessors to control electromechanical devices, biological
organisms use biochemical circuits to control molecular and chemical events.
The engineering and programming of biochemical circuits, in vivo and in
vitro, would transform industries that use chemical and nanostructured
materials. Although the construction of biochemical circuits has been
explored theoretically since the birth of molecular biology, our practical
experience with the capabilities and possible programming of biochemical
algorithms is still very young
- …