62,810 research outputs found
Algorithmic complexity for psychology: A user-friendly implementation of the coding theorem method
Kolmogorov-Chaitin complexity has long been believed to be impossible to
approximate when it comes to short sequences (e.g. of length 5-50). However,
with the newly developed \emph{coding theorem method} the complexity of strings
of length 2-11 can now be numerically estimated. We present the theoretical
basis of algorithmic complexity for short strings (ACSS) and describe an
R-package providing functions based on ACSS that will cover psychologists'
needs and improve upon previous methods in three ways: (1) ACSS is now
available not only for binary strings, but for strings based on up to 9
different symbols, (2) ACSS no longer requires time-consuming computing, and
(3) a new approach based on ACSS gives access to an estimation of the
complexity of strings of any length. Finally, three illustrative examples show
how these tools can be applied to psychology.Comment: to appear in "Behavioral Research Methods", 14 pages in journal
format, R package at http://cran.r-project.org/web/packages/acss/index.htm
Hamming distance kernelisation via topological quantum computation
We present a novel approach to computing Hamming distance and its kernelisation within Topological Quantum Computation. This approach is based on an encoding of two binary strings into a topological Hilbert space, whose inner product yields a natural Hamming distance kernel on the two strings. Kernelisation forges a link with the field of Machine Learning, particularly in relation to binary classifiers such as the Support Vector Machine (SVM). This makes our approach of potential interest to the quantum machine learning community
Hamming distance kernelisation via topological quantum computation
We present a novel approach to computing Hamming distance and its kernelisation within Topological Quantum Computation. This approach is based on an encoding of two binary strings into a topological Hilbert space, whose inner product yields a natural Hamming distance kernel on the two strings. Kernelisation forges a link with the field of Machine Learning, particularly in relation to binary classifiers such as the Support Vector Machine (SVM). This makes our approach of potential interest to the quantum machine learning community
Probabilistic initial value problem for cellular automaton rule 172
We consider the problem of computing a response curve for binary cellular
automata -- that is, the curve describing the dependence of the density of ones
after many iterations of the rule on the initial density of ones. We
demonstrate how this problem could be approached using rule 130 as an example.
For this rule, preimage sets of finite strings exhibit recognizable patterns,
and it is therefore possible to compute both cardinalities of preimages of
certain finite strings and probabilities of occurrence of these strings in a
configuration obtained by iterating a random initial configuration times.
Response curves can be rigorously calculated in both one- and two-dimensional
versions of CA rule 130. We also discuss a special case of totally disordered
initial configurations, that is, random configurations where the density of
ones and zeros are equal to 1/2.Comment: 13 pages, 3 figure
On the Complexity of Exact Pattern Matching in Graphs: Binary Strings and Bounded Degree
Exact pattern matching in labeled graphs is the problem of searching paths of
a graph that spell the same string as the pattern . This
basic problem can be found at the heart of more complex operations on variation
graphs in computational biology, of query operations in graph databases, and of
analysis operations in heterogeneous networks, where the nodes of some paths
must match a sequence of labels or types. We describe a simple conditional
lower bound that, for any constant , an -time or an -time algorithm for exact pattern
matching on graphs, with node labels and patterns drawn from a binary alphabet,
cannot be achieved unless the Strong Exponential Time Hypothesis (SETH) is
false. The result holds even if restricted to undirected graphs of maximum
degree three or directed acyclic graphs of maximum sum of indegree and
outdegree three. Although a conditional lower bound of this kind can be somehow
derived from previous results (Backurs and Indyk, FOCS'16), we give a direct
reduction from SETH for dissemination purposes, as the result might interest
researchers from several areas, such as computational biology, graph database,
and graph mining, as mentioned before. Indeed, as approximate pattern matching
on graphs can be solved in time, exact and approximate matching are
thus equally hard (quadratic time) on graphs under the SETH assumption. In
comparison, the same problems restricted to strings have linear time vs
quadratic time solutions, respectively, where the latter ones have a matching
SETH lower bound on computing the edit distance of two strings (Backurs and
Indyk, STOC'15).Comment: Using Lemma 12 and Lemma 13 might to be enough to prove Lemma 14.
However, the proof of Lemma 14 is correct if you assume that the graph used
in the reduction is a DAG. Hence, since the problem is already quadratic for
a DAG and a binary alphabet, it has to be quadratic also for a general graph
and a binary alphabe
Computation using Noise-based Logic: Efficient String Verification over a Slow Communication Channel
Utilizing the hyperspace of noise-based logic, we show two string
verification methods with low communication complexity. One of them is based on
continuum noise-based logic. The other one utilizes noise-based logic with
random telegraph signals where a mathematical analysis of the error probability
is also given. The last operation can also be interpreted as computing
universal hash functions with noise-based logic and using them for string
comparison. To find out with 10^-25 error probability that two strings with
arbitrary length are different (this value is similar to the error probability
of an idealistic gate in today's computer) Alice and Bob need to compare only
83 bits of the noise-based hyperspace.Comment: Accepted for publication in European Journal of Physics B (November
10, 2010
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