2,533 research outputs found

    Kolmogorov Complexity in perspective. Part II: Classification, Information Processing and Duality

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    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

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    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

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    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

    Semantic Storage: Overview and Assessment

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    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

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    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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