30,002 research outputs found
Complete Symmetry in D2L Systems and Cellular Automata
We introduce completely symmetric D2L systems and cellular automata by means of an additional restriction on the corresponding symmetric devices. Then we show that completely symmetric D2L systems and cellular automata are still able to simulate Turing machine computations. As corollaries we obtain new characterizations of the recursively enumerable languages and of some space-bounded complexity classes
Complexity of Two-Dimensional Patterns
In dynamical systems such as cellular automata and iterated maps, it is often
useful to look at a language or set of symbol sequences produced by the system.
There are well-established classification schemes, such as the Chomsky
hierarchy, with which we can measure the complexity of these sets of sequences,
and thus the complexity of the systems which produce them.
In this paper, we look at the first few levels of a hierarchy of complexity
for two-or-more-dimensional patterns. We show that several definitions of
``regular language'' or ``local rule'' that are equivalent in d=1 lead to
distinct classes in d >= 2. We explore the closure properties and computational
complexity of these classes, including undecidability and L-, NL- and
NP-completeness results.
We apply these classes to cellular automata, in particular to their sets of
fixed and periodic points, finite-time images, and limit sets. We show that it
is undecidable whether a CA in d >= 2 has a periodic point of a given period,
and that certain ``local lattice languages'' are not finite-time images or
limit sets of any CA. We also show that the entropy of a d-dimensional CA's
finite-time image cannot decrease faster than t^{-d} unless it maps every
initial condition to a single homogeneous state.Comment: To appear in J. Stat. Phy
On acceptance conditions for membrane systems: characterisations of L and NL
In this paper we investigate the affect of various acceptance conditions on
recogniser membrane systems without dissolution. We demonstrate that two
particular acceptance conditions (one easier to program, the other easier to
prove correctness) both characterise the same complexity class, NL. We also
find that by restricting the acceptance conditions we obtain a characterisation
of L. We obtain these results by investigating the connectivity properties of
dependency graphs that model membrane system computations
Algorithmic Complexity for Short Binary Strings Applied to Psychology: A Primer
Since human randomness production has been studied and widely used to assess
executive functions (especially inhibition), many measures have been suggested
to assess the degree to which a sequence is random-like. However, each of them
focuses on one feature of randomness, leading authors to have to use multiple
measures. Here we describe and advocate for the use of the accepted universal
measure for randomness based on algorithmic complexity, by means of a novel
previously presented technique using the the definition of algorithmic
probability. A re-analysis of the classical Radio Zenith data in the light of
the proposed measure and methodology is provided as a study case of an
application.Comment: To appear in Behavior Research Method
Active Self-Assembly of Algorithmic Shapes and Patterns in Polylogarithmic Time
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 molecular motors that
walk on rigid tracks and proteins that dynamically alter the structure of the
cell during mitosis, to embryonic development where large-scale complicated
organisms efficiently grow from a single cell. Using this active self-assembly
model, we show how to efficiently self-assemble shapes and patterns from simple
monomers. For example, we show how to grow a line of monomers in time and
number of monomer states that is merely logarithmic in the length of the line.
Our main results show how to grow arbitrary connected two-dimensional
geometric shapes and patterns in expected time that is polylogarithmic in the
size of the shape, plus roughly the time required to run a Turing machine
deciding whether or not a given pixel is in the shape. We do this while keeping
the number of monomer types logarithmic in shape size, plus those monomers
required by the Kolmogorov complexity of the shape or pattern. This work thus
highlights the efficiency advantages of active self-assembly over passive
self-assembly and motivates experimental effort to construct general-purpose
active molecular self-assembly systems
Archival Issues in Network Electronic Publications
published or submitted for publicatio
Development and application of computer software techniques to human factors task data handling problems Final report, 21 Jun. 1965 - 21 Jun. 1966
Computer software techniques applied to human factors task data handling problem
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