35,556 research outputs found
Self-Assembly of Infinite Structures
We review some recent results related to the self-assembly of infinite
structures in the Tile Assembly Model. These results include impossibility
results, as well as novel tile assembly systems in which shapes and patterns
that represent various notions of computation self-assemble. Several open
questions are also presented and motivated
Normal forms for Answer Sets Programming
Normal forms for logic programs under stable/answer set semantics are
introduced. We argue that these forms can simplify the study of program
properties, mainly consistency. The first normal form, called the {\em kernel}
of the program, is useful for studying existence and number of answer sets. A
kernel program is composed of the atoms which are undefined in the Well-founded
semantics, which are those that directly affect the existence of answer sets.
The body of rules is composed of negative literals only. Thus, the kernel form
tends to be significantly more compact than other formulations. Also, it is
possible to check consistency of kernel programs in terms of colorings of the
Extended Dependency Graph program representation which we previously developed.
The second normal form is called {\em 3-kernel.} A 3-kernel program is composed
of the atoms which are undefined in the Well-founded semantics. Rules in
3-kernel programs have at most two conditions, and each rule either belongs to
a cycle, or defines a connection between cycles. 3-kernel programs may have
positive conditions. The 3-kernel normal form is very useful for the static
analysis of program consistency, i.e., the syntactic characterization of
existence of answer sets. This result can be obtained thanks to a novel
graph-like representation of programs, called Cycle Graph which presented in
the companion article \cite{Cos04b}.Comment: 15 pages, To appear in Theory and Practice of Logic Programming
(TPLP
Approximate Computation and Implicit Regularization for Very Large-scale Data Analysis
Database theory and database practice are typically the domain of computer
scientists who adopt what may be termed an algorithmic perspective on their
data. This perspective is very different than the more statistical perspective
adopted by statisticians, scientific computers, machine learners, and other who
work on what may be broadly termed statistical data analysis. In this article,
I will address fundamental aspects of this algorithmic-statistical disconnect,
with an eye to bridging the gap between these two very different approaches. A
concept that lies at the heart of this disconnect is that of statistical
regularization, a notion that has to do with how robust is the output of an
algorithm to the noise properties of the input data. Although it is nearly
completely absent from computer science, which historically has taken the input
data as given and modeled algorithms discretely, regularization in one form or
another is central to nearly every application domain that applies algorithms
to noisy data. By using several case studies, I will illustrate, both
theoretically and empirically, the nonobvious fact that approximate
computation, in and of itself, can implicitly lead to statistical
regularization. This and other recent work suggests that, by exploiting in a
more principled way the statistical properties implicit in worst-case
algorithms, one can in many cases satisfy the bicriteria of having algorithms
that are scalable to very large-scale databases and that also have good
inferential or predictive properties.Comment: To appear in the Proceedings of the 2012 ACM Symposium on Principles
of Database Systems (PODS 2012
On the topological aspects of the theory of represented spaces
Represented spaces form the general setting for the study of computability
derived from Turing machines. As such, they are the basic entities for
endeavors such as computable analysis or computable measure theory. The theory
of represented spaces is well-known to exhibit a strong topological flavour. We
present an abstract and very succinct introduction to the field; drawing
heavily on prior work by Escard\'o, Schr\"oder, and others.
Central aspects of the theory are function spaces and various spaces of
subsets derived from other represented spaces, and -- closely linked to these
-- properties of represented spaces such as compactness, overtness and
separation principles. Both the derived spaces and the properties are
introduced by demanding the computability of certain mappings, and it is
demonstrated that typically various interesting mappings induce the same
property.Comment: Earlier versions were titled "Compactness and separation for
represented spaces" and "A new introduction to the theory of represented
spaces
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