2,533 research outputs found
Kolmogorov Complexity in perspective. Part II: Classification, Information Processing and Duality
We survey diverse approaches to the notion of information: from Shannon
entropy to Kolmogorov complexity. Two of the main applications of Kolmogorov
complexity are presented: randomness and classification. The survey is divided
in two parts published in a same volume. Part II is dedicated to the relation
between logic and information system, within the scope of Kolmogorov
algorithmic information theory. We present a recent application of Kolmogorov
complexity: classification using compression, an idea with provocative
implementation by authors such as Bennett, Vitanyi and Cilibrasi. This stresses
how Kolmogorov complexity, besides being a foundation to randomness, is also
related to classification. Another approach to classification is also
considered: the so-called "Google classification". It uses another original and
attractive idea which is connected to the classification using compression and
to Kolmogorov complexity from a conceptual point of view. We present and unify
these different approaches to classification in terms of Bottom-Up versus
Top-Down operational modes, of which we point the fundamental principles and
the underlying duality. We look at the way these two dual modes are used in
different approaches to information system, particularly the relational model
for database introduced by Codd in the 70's. This allows to point out diverse
forms of a fundamental duality. These operational modes are also reinterpreted
in the context of the comprehension schema of axiomatic set theory ZF. This
leads us to develop how Kolmogorov's complexity is linked to intensionality,
abstraction, classification and information system.Comment: 43 page
On the Complexity of Nonrecursive XQuery and Functional Query Languages on Complex Values
This paper studies the complexity of evaluating functional query languages
for complex values such as monad algebra and the recursion-free fragment of
XQuery.
We show that monad algebra with equality restricted to atomic values is
complete for the class TA[2^{O(n)}, O(n)] of problems solvable in linear
exponential time with a linear number of alternations. The monotone fragment of
monad algebra with atomic value equality but without negation is complete for
nondeterministic exponential time. For monad algebra with deep equality, we
establish TA[2^{O(n)}, O(n)] lower and exponential-space upper bounds.
Then we study a fragment of XQuery, Core XQuery, that seems to incorporate
all the features of a query language on complex values that are traditionally
deemed essential. A close connection between monad algebra on lists and Core
XQuery (with ``child'' as the only axis) is exhibited, and it is shown that
these languages are expressively equivalent up to representation issues. We
show that Core XQuery is just as hard as monad algebra w.r.t. combined
complexity, and that it is in TC0 if the query is assumed fixed.Comment: Long version of PODS 2005 pape
Domain-independent queries on databases with external functions
AbstractWe study queries over databases with external functions, from a language-independent perspective. The input and output types of the external functions can be atomic values, flat relations, nested relations, etc. We propose a new notion of data-independence for queries on databases with external functions, which extends naturally the notion of generic queries on relational databases without external functions. In contrast to previous such notions, ours can also be applied to queries expressed in query languages with iterations. Next, we propose two natural notions of computability for queries over databases with external functions, and prove that they are equivalent, under reasonable assumptions. Thus, our definition of computability is robust. Finally, based on this equivalence result, we give examples of complete query languages with external functions. A byproduct of the equivalence result is the fact that Relational Machines (Abiteboul and V. Vianu, 1991; Abiteboul et al., 1992) are complete on nested relations: they are known not to be complete on flat relations
An introduction to Graph Data Management
A graph database is a database where the data structures for the schema
and/or instances are modeled as a (labeled)(directed) graph or generalizations
of it, and where querying is expressed by graph-oriented operations and type
constructors. In this article we present the basic notions of graph databases,
give an historical overview of its main development, and study the main current
systems that implement them
Semantic Storage: Overview and Assessment
The Semantic Web has a great deal of momentum behind it. The promise of a ‘better web’, where information is given well defined meaning and computers are better able to work with it has captured the imagination of a significant number of people, particularly in academia. Language standards such as RDF and OWL have appeared with remarkable speed, and development continues apace. To back up this development, there is a requirement for ‘semantic databases’, where this data can be conveniently stored, operated upon, and retrieved. These already exist in the form of triple stores, but do not yet fulfil all the requirements that may be made of them, particularly in the area of performing inference using OWL. This paper analyses the current stores along with forthcoming technology, and finds that it is unlikely that a combination of speed, scalability, and complex inferencing will be practical in the immediate future. It concludes by suggesting alternative development routes
Logic Programming as Constructivism
The features of logic programming that
seem unconventional from the viewpoint of classical logic
can be explained in terms of constructivistic logic. We
motivate and propose a constructivistic proof theory of
non-Horn logic programming. Then, we apply this formalization
for establishing results of practical interest.
First, we show that 'stratification can be motivated in a
simple and intuitive way. Relying on similar motivations,
we introduce the larger classes of 'loosely stratified' and
'constructively consistent' programs. Second, we give a
formal basis for introducing quantifiers into queries and
logic programs by defining 'constructively domain
independent* formulas. Third, we extend the Generalized
Magic Sets procedure to loosely stratified and constructively
consistent programs, by relying on a 'conditional
fixpoini procedure
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