47,555 research outputs found
Algebraic optimization of recursive queries
Over the past few years, much attention has been paid to deductive databases. They offer a logic-based interface, and allow formulation of complex recursive queries. However, they do not offer appropriate update facilities, and do not support existing applications. To overcome these problems an SQL-like interface is required besides a logic-based interface.\ud
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In the PRISMA project we have developed a tightly-coupled distributed database, on a multiprocessor machine, with two user interfaces: SQL and PRISMAlog. Query optimization is localized in one component: the relational query optimizer. Therefore, we have defined an eXtended Relational Algebra that allows recursive query formulation and can also be used for expressing executable schedules, and we have developed algebraic optimization strategies for recursive queries. In this paper we describe an optimization strategy that rewrites regular (in the context of formal grammars) mutually recursive queries into standard Relational Algebra and transitive closure operations. We also describe how to push selections into the resulting transitive closure operations.\ud
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The reason we focus on algebraic optimization is that, in our opinion, the new generation of advanced database systems will be built starting from existing state-of-the-art relational technology, instead of building a completely new class of systems
Baxter operator formalism for Macdonald polynomials
We develop basic constructions of the Baxter operator formalism for the
Macdonald polynomials associated with root systems of type A. Precisely we
construct a dual pair of mutually commuting Baxter operators such that the
Macdonald polynomials are their common eigenfunctions. The dual pair of Baxter
operators is closely related to the dual pair of recursive operators for
Macdonald polynomials leading to various families of their integral
representations. We also construct the Baxter operator formalism for the
q-deformed gl(l+1)-Whittaker functions and the Jack polynomials obtained by
degenerations of the Macdonald polynomials associated with the type A_l root
system. This note provides a generalization of our previous results on the
Baxter operator formalism for the Whittaker functions. It was demonstrated
previously that Baxter operator formalism for the Whittaker functions has deep
connections with representation theory. In particular the Baxter operators
should be considered as elements of appropriate spherical Hecke algebras and
their eigenvalues are identified with local Archimedean L-factors associated
with admissible representations of reductive groups over R. We expect that the
Baxter operator formalism for the Macdonald polynomials has an interpretation
in representation theory of higher-dimensional arithmetic fields.Comment: 22 pages, typos are fixe
Proof-irrelevant model of CC with predicative induction and judgmental equality
We present a set-theoretic, proof-irrelevant model for Calculus of
Constructions (CC) with predicative induction and judgmental equality in
Zermelo-Fraenkel set theory with an axiom for countably many inaccessible
cardinals. We use Aczel's trace encoding which is universally defined for any
function type, regardless of being impredicative. Direct and concrete
interpretations of simultaneous induction and mutually recursive functions are
also provided by extending Dybjer's interpretations on the basis of Aczel's
rule sets. Our model can be regarded as a higher-order generalization of the
truth-table methods. We provide a relatively simple consistency proof of type
theory, which can be used as the basis for a theorem prover
Probability-guaranteed H∞ finite-horizon filtering for a class of nonlinear time-varying systems with sensor saturations
This is the Post-Print version of the Article. The official published version can be accessed from the link below - Copyright @ 2012 ElsevierIn this paper, the probability-guaranteed H∞ finite-horizon filtering problem is investigated for a class of nonlinear time-varying systems with uncertain parameters and sensor saturations. The system matrices are functions of mutually independent stochastic variables that obey uniform distributions over known finite ranges. Attention is focused on the construction of a time-varying filter such that the prescribed H∞ performance requirement can be guaranteed with probability constraint. By using the difference linear matrix inequalities (DLMIs) approach, sufficient conditions are established to guarantee the desired performance of the designed finite-horizon filter. The time-varying filter gains can be obtained in terms of the feasible solutions of a set of DLMIs that can be recursively solved by using the semi-definite programming method. A computational algorithm is specifically developed for the addressed probability-guaranteed H∞ finite-horizon filtering problem. Finally, a simulation example is given to illustrate the effectiveness of the proposed filtering scheme.This work was supported in part by the National Natural Science Foundation of China under Grants 61028008, 60825303 and
60834003, National 973 Project under Grant 2009CB320600, the Fok Ying Tung Education Fund under Grant 111064, the Special Fund for the Author of National Excellent Doctoral Dissertation of China under Grant 2007B4, the Key Laboratory of Integrated
Automation for the Process Industry (Northeastern University) from the Ministry of Education of China, the Engineering and
Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., and the
Alexander von Humboldt Foundation of Germany
Beating the Productivity Checker Using Embedded Languages
Some total languages, like Agda and Coq, allow the use of guarded corecursion
to construct infinite values and proofs. Guarded corecursion is a form of
recursion in which arbitrary recursive calls are allowed, as long as they are
guarded by a coinductive constructor. Guardedness ensures that programs are
productive, i.e. that every finite prefix of an infinite value can be computed
in finite time. However, many productive programs are not guarded, and it can
be nontrivial to put them in guarded form.
This paper gives a method for turning a productive program into a guarded
program. The method amounts to defining a problem-specific language as a data
type, writing the program in the problem-specific language, and writing a
guarded interpreter for this language.Comment: In Proceedings PAR 2010, arXiv:1012.455
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