关系代数派生算子语义表达式间等价性证明

关系代数的派生算子在关系数据库查询语言中得到了广泛应用。它们的语义有两种常见的表示方式,一种是基于原始算子的表达式,一种是基于一阶逻辑的表达式。但有关的文献资料都没有给出这两种表达式等价性的严格证明。文章尝试通过一系列等价变换,证明派生算子语义的这两种表达式间的等价性。从派生算子（主要是除算子）语义的原始算子表达式出发,根据关系代数表达式的特点,通过一步步的等价变换,得到派生算子语义的一阶逻辑表达式。所使用的变换方法能为关系代数表达式的正确性证明打下基础。     

分布式数据库查询优化处理——基于关系代数等价变换的查询优化处理

在进行分布式数据库应用时，快速而准确的得到查询结果一直是分布式数据库得以应用的关键问题。本文阐述了分布式查询优化的一种策略和算法——基于关系代数等价变换的查询优化处理。     

基于关系代数的分布式数据库查询优化

分布式数据库系统由于其数据的物理分布和冗余特性,使得对于分布式数据库的查询优化处理难度更大和复杂度更高,而分布式数据库查询优化处理一直是分布式数据库主要研究问题之一。本文主要概括地介绍分布式数据库查询过程、查询优化的策略和目标,重点阐述了基于关系代数等价变换的分布式数据库查询优化算法。     

关系代数表达式写法的新教学方法

在《数据库系统原理》的教学中,重难点之一是利用关系代数语言表示关系的查询操作。该文提出了一种基于人眼移动的关系代数表达式书写方法,该方法将抽象难懂的数学概念转换为学生易于理解的方式,有助于学生理解关系代数表达式的结构,并快速正确地书写关系代数表达式,在实际教学中取得了良好的效果。     

时态关系代数与元组演算的等价性

建立了一个时态关系代数和时态元组演算并证明了他们间的等价性。     

基于范算子的模糊逻辑及等价关系语义

讨论了范算子的使用方法和特点,提出了基于范算子的模糊逻辑和推理,讨论合取通过t-norm来计算,对等值、等价和模糊集合的语义也进行了研究讨论,同时利用等价关系理论对模糊环境进行说明,并给出了几个具体例子.     

高阶惯性环节代数等价观测器简易转换方法

为快速计算出代数等价观测器(AEO)的参数对控制系统的影响,基于高阶惯性环节代数等价观测器工程应用的实际,并参照矩阵的Jordan标准型,定义了广义Jordan型矩阵块JBS,通过数学分析给出转换矩阵P的简捷计算方法,为揭示AEO之间的内在关系提供一个有效途径。该方法不仅有助于调节系统的设计,而且通过适当的运用,还能使其达到更加有益的效果。在某电厂600 MW单元机组锅炉过热器蒸汽温度调节系统中的应用案例,证明了所提方法的实用性和有效性。     

用SQL实现关系代数中近似除与关系整除方法的研究

关系代数是关系数据库的理论推演代数基础,而SQL是具体实现的标准计算机语言,特别是关系代数之中的除问题,很多情况下仅仅是理论抽象代数形式。本文通过对关系代数的深入剖析,分解为近似除和关系整除,通过实际案例进行关系代数除运算比较和推演,并最终通过SQL实现。     

Time-based operators for relational algebra query languages

We present a new approach for historical relational algebra languages based upon generalized logic for Boolean and comparison operators and a temporal modification of the standard relational algebra operators. Historical versions of standard (snapshot) relational algebra operators based upon this generalized logic are presented. The temporal modification employs a logic that operates on sets of value/time-interval pairs and which can be applied to snapshot as well as historical databases. Our emphasis is that the generalized operators can be used to enrich existing historical query languages and to provide an easier and more natural time-based interface. Using the generalized operators, users can express their queries more naturally, succinctly and elegantly. Examples are presented which illustrate that the modified operators offer a good degree of flexibility in expressing different temporal requirements.     

Strong equivalence of relational expressions under dependencies

We propose two-well founded orderings on multisets that extend the Dershowitz-Manna ordering. Unlike the Dershowitz-Manna ordering, ours do not have a natural monotonicity property. This lack of monotonicity suggests using monotonicity to provide a new characterization of the Dershowitz-Manna ordering. Section 5 proposes an efficient and correct implementation of that ordering.     

On the expressive power of the relational algebra with partially ordered domains

Assuming data domains are partially ordered, we define the partially ordered relational algebra (PORA) by allowing the ordering predicate ? to be used in formulae of the selection operator σ. We apply Paredaens and Bancilhon's Theorem to examine the expressiveness of the PORA, and show that the PORA expresses exactly the set of all possible relations which are invariant under order-preserving automorphisms of databases. The extension is consistent with the two important extreme cases of unordered and linearly ordered domains. We also investigate the three hierarchies of: (1) computable queries, (2) query languages and (3) partially ordered domains, and show that there is a one-to-one correspondence between them.     

Fuzzy relational algebra for possibility-distribution-fuzzy-relational model of fuzzy data

In the real world, there exist a lot of fuzzy data which cannot or need not be precisely defined. We distinguish two types of fuzziness: one in an attribute value itself and the other in an association of them. For such fuzzy data, we propose a possibility-distribution-fuzzy-relational model, in which fuzzy data are represented by fuzzy relations whose grades of membership and attribute values are possibility distributions. In this model, the former fuzziness is represented by a possibility distribution and the latter by a grade of membership. Relational algebra for the ordinary relational database as defined by Codd includes the traditional set operations and the special relational operations. These operations are classified into the primitive operations, namely, union, difference, extended Cartesian product, selection and projection, and the additional operations, namely, intersection, join, and division. We define the relational algebra for the possibility-distribution-fuzzy-relational model of fuzzy databases.     

Validation of HOL Proofs by Proof Checking

Formal proofs generated by mechanised theorem proving systems may consist of a large number of inferences. As these theorem proving systems are usually very complex, it is extremely difficult if not impossible to formally verify them. This calls for an independent means of ensuring the consistency of mechanically generated proofs. This paper describes a method of recording HOL proofs in terms of a sequence of applications of inference rules. The recorded proofs can then be checked by an independent proof checker. Also described in this paper is an implementation of a proof checker which is able to check a practical proof consisting of thousands of inference steps.     

Algebras of modal operators and partial correctness

Modal Kleene algebras are Kleene algebras enriched by forward and backward box and diamond operators. We formalise the symmetries of these operators as Galois connections, complementarities and dualities. We study their properties in the associated operator algebras and show that the axioms of relation algebra are theorems at the operator level. Modal Kleene algebras provide a unifying semantics for various program calculi and enhance efficient cross-theory reasoning in this class, often in a very concise pointfree style. This claim is supported by novel algebraic soundness and completeness proofs for Hoare logic and by connecting this formalism with an algebraic decision procedure.     

Comparison of fuzzy implication operators by means of fuzzy relational products used for intelligent local path-planning of AUVs

This paper describes the best choice to fuzzy implication operator and α-cut that are proper to the heuristic search technique for real-time collision avoidance of autonomous underwater vehicles (AUVs). A fuzzy implication operator is applied to the computation of fuzzy triangle product that constructs a new fuzzy relation between two fuzzy relations. An α-cut transforms a fuzzy relation into a crisp relation which is represented as a matrix. Those are the theoretical basis of heuristic search technique. In this paper, we review briefly our previous work—a heuristic search technique using fuzzy relational products for the collision avoidance system of AUVs, and propose the selection of a fuzzy implication operator and α-cut which are the most suitable for the search technique. In order to verify the optimality and the efficiency of the selected fuzzy implication operator and α-cut, we simulate every case of α-cut for each fuzzy implication operator in view of the cost of path and the number of α -cut generating acceptable path to the goal. This work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2007-521-D00433).     

Iterated Bernstein operators for distribution function and density estimation: Balancing between the number of iterations and the polynomial degree

Despite its slow convergence, the use of the Bernstein polynomial approximation is becoming more frequent in Statistics, especially for density estimation of compactly supported probability distributions. This is due to its numerous attractive properties, from both an approximation (uniform shape-preserving approximation, etc.) and a statistical (bona fide estimation, low boundary bias, etc.) point of view. An original method for estimating distribution functions and densities with Bernstein polynomials is proposed, which takes advantage of results about the eigenstructure of the Bernstein operator to refine a convergence acceleration method. Furthermore, an original data-driven method for choosing the degree of the polynomial is worked out. The method is successfully applied to two data-sets which are important benchmarks in the field of Density Estimation.