Linearization of nonlinear recursive rules

The problem of converting a simple nonlinear recursive logic query into an equivalent linear one is considered. A general method is given to transform a nonlinear rule into a sequence of linear ones. For efficient processing it is necessary to convert a nonlinear rule into a single linear rule. For such a conversion, a necessary and sufficient condition is provided for a type of doubly recursive rule to be equivalent to the resulting linear rule. It is also shown that a restricted type of higher order recursive rule is equivalent to the linear rule obtained by its conversion     

Proof rules for recursive procedures

Four proof rules for recursive procedures in a Pascal-like language are presented. The main rule deals with total correctness and is based on results of Gries and Martin. The rule is easier to apply than Martin's. It is introduced as an extension of a specification format for Pascal-procedures, with its associated correctness and invocation rules. It uses well-founded recursion and is proved under the postulate that a procedure is semantically equal to its body.This rule for total correctness is compared with Hoare's rule for partial correctness of recursive procedures, in which no well-founded relation is needed. Both rules serve to prove correctness, i.e. sufficiency of certain preconditions. There are also two rules for proving necessity of preconditions. These rules can be used to give formal proofs of nontermination and refinement. They seem to be completely new.     

Evaluation of recursive queries with extended rules in deductivedatabases

In order to extend the expressive power of deductive databases, a formula that can have existential quantifiers in prenex normal form in a restricted way is defined as an extended rule. With the extended rule, we can easily define a virtual view that requires a division operation of relational algebra to evaluate. The paper addresses a recursive query evaluation where at least one formula in a recursive rule set is of an extended rule. We investigate transformable recursions as well as four cases of non-transformable recursions of transitive-closure-like and linear type. The work reveals that occurrence of an existentially quantified variable in the extended recursive body predicate might dramatically limit the level of recursive search. In particular, the number of iterations to answer extended queries can be determined, independently of database contents     

Inference rules for proving the equivalence of recursive procedures

Inspired by Hoare’s rule for recursive procedures, we present three proof rules for the equivalence between recursive programs. The first rule can be used for proving partial equivalence of programs; the second can be used for proving their mutual termination; the third rule can be used for proving the equivalence of reactive programs. There are various applications to such rules, such as proving equivalence of programs after refactoring and proving backward compatibility.     

一种精简的关联规则表示模型

针对关联规则之间存在的冗余性问题,已提出多种精简关联规则模型,但这些模型仍不同程度存在紧致度欠佳、信息丢失或恢复算法复杂的问题.提出了一种含更丰富关联信息的基本关联规则,并以基本关联规则为基础构建无损的精简关联规则集合,它是原始关联规则集合的子集,并能据此完全恢复原始关联规则集合.给出了基本关联规则模型的定义,证明了该精简模型的几个重要性质,并设计了用于挖掘该类规则的挖掘算法.实验表明,基本关联规则模型比现有的关联规则精简模型更加紧致.     

The representation of fuzzy relational production rules

We look at the representation within the framework of the approximate reasoning of relational type rules. A relational production rule consists of a rule in which one of the antecedent requirements involves the satisfaction of a relationship between two variables. An example of this type of rule is if lower and upper bounds are close then the uncertainty is low.     

Simulation of linear decision rules

Linearized decision rules in the aggregate production scheduling framework are compared through simulation experiments to see if decisions are improved when adaptive feedback elements are built into the rule. Our results, based on some non-parametric tests, show the need for determining an optimal trade-off between stabilization and experimentation through a specified cost functional.     

一个线性递归查询算法的设计与实现

旨在解决在演绎数据库中,如何利用递归规则进行递归查询的问题。介绍了一个线性递归查询算法的基本思想,阐述了该算法的设计与具体实现,包括算法采用的数据结构、程序中各功能模块的功能,对算法进行了分析。     

Robust recursive identification of multidimensional linear regression models

Stochastic adaptive estimation and control algorithms involving recursive prediction estimates have guaranteed convergence rates when the noise is not ‘too’ coloured, as when a positive-real condition on the noise mode is satisfied. Moreover, the whiter the noise environment the more robust are the algorithms. This paper shows that for linear regression signal models, the suitable introduction of while noise into the estimation algorithm can make it more robust without compromising on convergence rates. Indeed, there are guaranteed attractive convergence rates independent of the process noise colour. No positive-real condition is imposed on the noise model.     

基于迭代神经网络的图像结构表示和分类

由于缺少结构化的表示,基于内容的图像分类存在一定的问题,据此提出了一种基于迭 代神经网络的自然图像表示和分类的方法。利用Berkeley分割算法将图像分割成不同的区域,采用 基于人工的多叉树或基于邻接区域的二叉树的方法进行区域合并,同时提取区域统计特征,得到图像 的树型结构表示。根据BPTS算法对网络进行训练,训练好的网络就具备了图像分类的功能。实验 结果表明,基于迭代神经网络的结构表示和分类方法具有很强的结构学习能力,同时人工生成的多叉 树涵盖更多的语义信息且能得到较好的分类结果。     

Optimal linear recursive estimation with uncertain system parameters

In an estimation problem the statistics of various random processes involved may not be known exactly. Using linear state space modeling techniques, this lack of information can often be represented by allowing certain system model parameters to assume any of a finite set of possible known values with corresponding a priori known probabilities. In this short paper a recursive minimum variance estimator, restricted to be a linear function of the observation data sequence, is obtained for an estimation problem which can be described by a linear discrete time system model with uncertain parameters; all initial information relative to these uncertain parameters is utilized by the estimator. The estimation error covariance matrix, in a recursive form, is also obtained. An example is given to illustrate the usefulness of this estimator.     

Polyhedral representation of fuzzy linear bases

 In [15], we introduced the concepts of fuzzy bases, fuzzy linear interpolation and fuzzy polygon of four-component fuzzy linear bases. In [16], these concepts were used in the maximal profile of the set of polygons generated from a set of break points for each variable dimension. Theconcept was operationalized in a fuzzy linear basis algorithm (FLBA) for nonlinear separable programming problems involving no more than a finite number of discontinuities. The FLBA provides a powerful platform forparallel processing of the fuzzy linear sub-problems included in the finite FLB-chain. In this paper we extend the theory of fuzzy linear bases from the set of polygons toapolyhedral representation of four-component fuzzy linear bases defined on a closed subset of the real line.     

A global representation of the recursive functions in the λ-calculus

The class of monotonic (in the sense of Scott) functions is divided into subclasses of sequential and parallel ones and the problem of comparative power of different sequential and parallel functions with respect to composition (Theorems 1–5) and recursion (Theorem 6) is then investigated. In particular, Theorem 6 answers the question of Scott concerning the power of his Logic for Computable Functions.     

Singular control of stochastic linear systems with recursive utility

We formulate a class of singular stochastic control problem with recursive utility where the cost function is determined by a backward stochastic differential equation. Some characteristics of the value function of the control problem are obtained by the method of approximation via penalization, and the optimal control process is constructed.     

Classification and compilation of linear recursive queries indeductive databases

The authors present a graph model which is powerful in classifying and compiling linear recursive formulas in deductive databases. The graph model consists of two kinds of graphs: I-graph and resolution graph. Essential properties of a recursive formula can be extracted from its I-graph, and the compiled formula and the query evaluation plan of the recursive formulas can be determined from its resolution graph. It is demonstrated that based on the graph model all the linear recursive formulas can be classified into a taxonomy of classes and each class shares common characteristics in query compilation and query processing. The compiled formulas and the corresponding query evaluation plans can be derived based on the study of the compilation of each class     

On representation of source reliability through weights on rules

Rule-based expert systems often require their users assess the state of an event and then “report” to the system that state. the system then uses that report of the event as the basis of inference, that is, the hypothesis. the problem is that the report is just that, a report. the report is not necessarily the same as the underlying event that occurred. the relationship between the report and the underlying event is referred to as the reliability of the report or the credibility of the report. This article integrates the difference between the report and the underlying event into the weights of two different uncertainty representation schemes used in expert systems. In each case the impact of that reliability is explored. For example, it is found that the model without reliability is equivalent to the model with reliability, in the case of complete reliability. Further, in some cases the weights are monotonic functions of reliability. Accounting for reliability is found to have a substantial impact on the value of the weights. Further, one approach is seen as influenced less by a lack of reliability than another approach.     

Adaptive control with recursive identification for stochastic linear systems

This paper presents a stochastic adaptive control algorithm which is shown to possess the following properties when applied to a possibly unstable, inverse stable, linear stochastic system with unknown parameters, whenever that system satisfies a certain positive real condition on its (moving average) noise dynamics. 1) The adaptive control part of the algorithm stabilizes and asymptotically optimizes the behavior of the system in the sense that the (limit of the) sample mean-square variation of the-output around a given demand level equals that of a minimum variance control strategy implemented with known parameters. This optimal behavior is subject to an offset μ²where μ²is the variance of a dither signal added to the control action in order to produce a "continually disturbed control." Formu^{2} > 0, it is shown that the input-output process satisfies a persistent excitation property, and hence, subject to a simple identifiability condition, the next property holds. 2) The observed input and output of the controlled system may be taken as inputs to an approximate maximum likelihood algorithm (AML) which generates strongly consistent estimates of the system's parameters. Results are presented for the scalar and multivariable cases.     

An efficient representation for linear constraints

An efficient representation for the linear constraints generated by a recent CACSD (computer-aided control system design) method has been developed. The linear constraints arise from engineering constraints on the time- and frequency-domain responses of the closed-loop system. The representation reduces the storage requirements and improves the efficiency of the quadratic programming algorithm used by the design method. The algorithm performs two distinct operations on the individual constraints. The first determines if a constraint has been satisfied and the second is the computation of the distance in a specified search direction     

Generalized linear recursive networks: topological and routing properties

This paper presents a methodology for generalizing the class of linear recursive networks (LRN) reported by Hsu et al. [IEEE Trans Parallel Distrib Syst 1997; 8(7)]. The proposed generalization relaxes the restriction on the number of isomorphic subgraphs of LRNs, which is at most 1 by Hsu et al. [IEEE Trans Parallel Distrib Syst 1997; 8(7)]. Hence, our methodology permits the design of a communication topology of size n which satisfies the linear recurrence equation G_n(A)=a₁G_n−1(A)∪a₂G_n−2(A)∪?∪a_kG_n−k(A), with a_j being any non-negative integer for each j∈{1,2,…,k} and a₁>0. In addition, we address the problem of routing of messages in an generalized linear recursive network (GLRN). The paradigm of Fibonacci cubes (FCs) is used to demonstrate the proposed technique. FCs were introduced recently as an attractive alternative to the well-known hypercube model for interconnection networks.A generalized FC, referred to as a “Fibonacci graph” (FG) of size n, is composed of an arbitrary number of such graphs of size n−1 and size n−2.The structural advantage of GLRNs, in general, and FG, in particular, manifests itself in the following ways:

1.

They allow more choices to construct systems of various sizes.

2.

They emulate other topologies, such as hypercubes, trees, rings and meshes very efficiently.

The results of this paper have important applications e.g. in multitasking and job scheduling where a job is decomposed into a set of tasks and assigned to a subset of processors with specified interconnection topology.