4,201 research outputs found
Density Classification Quality of the Traffic-majority Rules
The density classification task is a famous problem in the theory of cellular
automata. It is unsolvable for deterministic automata, but recently solutions
for stochastic cellular automata have been found. One of them is a set of
stochastic transition rules depending on a parameter , the
traffic-majority rules.
Here I derive a simplified model for these cellular automata. It is valid for
a subset of the initial configurations and uses random walks and generating
functions. I compare its prediction with computer simulations and show that it
expresses recognition quality and time correctly for a large range of
values.Comment: 40 pages, 9 figures. Accepted by the Journal of Cellular Automata.
(Some typos corrected; the numbers for theorems, lemmas and definitions have
changed with respect to version 1.
On the Algorithmic Nature of the World
We propose a test based on the theory of algorithmic complexity and an
experimental evaluation of Levin's universal distribution to identify evidence
in support of or in contravention of the claim that the world is algorithmic in
nature. To this end we have undertaken a statistical comparison of the
frequency distributions of data from physical sources on the one
hand--repositories of information such as images, data stored in a hard drive,
computer programs and DNA sequences--and the frequency distributions generated
by purely algorithmic means on the other--by running abstract computing devices
such as Turing machines, cellular automata and Post Tag systems. Statistical
correlations were found and their significance measured.Comment: Book chapter in Gordana Dodig-Crnkovic and Mark Burgin (eds.)
Information and Computation by World Scientific, 2010.
(http://www.idt.mdh.se/ECAP-2005/INFOCOMPBOOK/). Paper website:
http://www.mathrix.org/experimentalAIT
Empirical Encounters with Computational Irreducibility and Unpredictability
There are several forms of irreducibility in computing systems, ranging from
undecidability to intractability to nonlinearity. This paper is an exploration
of the conceptual issues that have arisen in the course of investigating
speed-up and slowdown phenomena in small Turing machines. We present the
results of a test that may spur experimental approaches to the notion of
computational irreducibility. The test involves a systematic attempt to outrun
the computation of a large number of small Turing machines (all 3 and 4 state,
2 symbol) by means of integer sequence prediction using a specialized function
finder program. This massive experiment prompts an investigation into rates of
convergence of decision procedures and the decidability of sets in addition to
a discussion of the (un)predictability of deterministic computing systems in
practice. We think this investigation constitutes a novel approach to the
discussion of an epistemological question in the context of a computer
simulation, and thus represents an interesting exploration at the boundary
between philosophical concerns and computational experiments.Comment: 18 pages, 4 figure
Flexible RNA design under structure and sequence constraints using formal languages
The problem of RNA secondary structure design (also called inverse folding)
is the following: given a target secondary structure, one aims to create a
sequence that folds into, or is compatible with, a given structure. In several
practical applications in biology, additional constraints must be taken into
account, such as the presence/absence of regulatory motifs, either at a
specific location or anywhere in the sequence. In this study, we investigate
the design of RNA sequences from their targeted secondary structure, given
these additional sequence constraints. To this purpose, we develop a general
framework based on concepts of language theory, namely context-free grammars
and finite automata. We efficiently combine a comprehensive set of constraints
into a unifying context-free grammar of moderate size. From there, we use
generic generic algorithms to perform a (weighted) random generation, or an
exhaustive enumeration, of candidate sequences. The resulting method, whose
complexity scales linearly with the length of the RNA, was implemented as a
standalone program. The resulting software was embedded into a publicly
available dedicated web server. The applicability demonstrated of the method on
a concrete case study dedicated to Exon Splicing Enhancers, in which our
approach was successfully used in the design of \emph{in vitro} experiments.Comment: ACM BCB 2013 - ACM Conference on Bioinformatics, Computational
Biology and Biomedical Informatics (2013
Новый генератор псевдослучайных последовательностей чисел на основе клеточного автомата
Розглядається новий генератор псевдовипадкових послідовностей біт, який реалізований на клітинному автоматі. Представлена апаратна реалізація генератора і виконано його програмне моделювання. За допомогою програмної моделі проведене тестування розробленого генератора псевдовипадкових чисел. Використані тести показали позитивний результат, який підтверджує високі статистичні властивості сформованої випадкової послідовності.This paper considers a novel pseudo-random bit sequence generator, which is implemented on a cellular automaton. It presents the hardware implementation of the generator and it the software simulation. With the help of the software model is testing of the random number generator was conducted. Tests showed a positive result, which confirms the high statistical properties of the generated random sequence.Рассматривается новый генератор псевдослучайных последовательностей бит, который реализован на клеточном автомате. Представлена аппаратная реализация генератора и выполнено его программное моделирование. С помощью программной модели проведено тестирование разработанного генератора псевдослучайных чисел. Использованные тесты показали положительный результат, который подтверждает высокие статистические свойства сформированной случайной последовательности
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Layered cellular automata for pseudorandom number generation
The proposed Layered Cellular Automata (L-LCA), which comprises of a main CA with L additional layers of memory registers, has simple local interconnections and high operating speed. The time-varying L-LCA transformation at each clock can be reduced to a single transformation in the set formed by the transformation matrix of a maximum length Cellular Automata (CA), and the entire transformation sequence for a single period can be obtained. The analysis for the period characteristics of state sequences is simplified by analyzing representative transformation sequences determined by the phase difference between the initial states for each layer. The L-LCA model can be extended by adding more layers of memory or through the use of a larger main CA based on widely available maximum length CA. Several L-LCA (L=1,2,3,4) with 10- to 48-bit main CA are subjected to the DIEHARD test suite and better results are obtained over other CA designs reported in the literature. The experiments are repeated using the well-known nonlinear functions and in place of the linear function used in the L-LCA. Linear complexity is significantly increased when or is used
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