Computation of Minimal Siphons in Petri Nets Using Problem Partitioning Approaches

A large amount of research has shown the vitality of siphon enumeration in the analysis and control of deadlocks in various resource-allocation systems modeled by Petri nets(PNs).In this paper,we propose an algorithm for the enumeration of minimal siphons in PN based on problem decomposition.The proposed algorithm is an improved version of the global partitioning minimal-siphon enumeration(GPMSE)proposed by Cordone et al.(2005)in IEEE Transactions on Systems,Man,and Cybernetics-Part A:Systems and Humans,which is widely used in the literature to compute minimal siphons.The experimental results show that the proposed algorithm consumes lower computational time and memory compared with GPMSE,which becomes more evident when the size of the handled net grows.

An iterative algorithm for solving ill-conditioned linear least squares problems

Linear Least Squares（LLS） problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics and geosciences, where regularization algorithms are employed to seek optimal solutions. For many problems, even with the use of regularization algorithms it may be impossible to obtain an accurate solution. Riley and Golub suggested an iterative scheme for solving LLS problems. For the early iteration algorithm, it is difficult to improve the well-conditioned perturbed matrix and accelerate the convergence at the same time. Aiming at this problem, self-adaptive iteration algorithm（SAIA） is proposed in this paper for solving severe ill-conditioned LLS problems. The algorithm is different from other popular algorithms proposed in recent references. It avoids matrix inverse by using Cholesky decomposition, and tunes the perturbation parameter according to the rate of residual error decline in the iterative process. Example shows that the algorithm can greatly reduce iteration times, accelerate the convergence,and also greatly enhance the computation accuracy.

AN ITERATIVE PROCEDURE FOR DOMAIN DECOMPOSITION METHOD OF SECOND ORDER ELLIPTIC PROBLEM WITH MIXED BOUNDARY CONDITIONS

This paper is devoted to study of an iterative procedure for domain decomposition method of second order elliptic problem with mixed boundary conditions (i.e., Dirichlet condition on a part of boundary and Neumann condition on the another part of boundary). For the pure Dirichlet problem, Marini and Quarteroni [3], [4] considered a similar approach, which is extended to more complex problem in this paper.

ON THE DECOMPOSITION PROBLEM OF STABILITY FOR VOLTERRA INTEGRODIFFERENTIAL EQUATIONS

In this paper, we discuss the problem of stability of Volterra integrodifferential equationwith the decompositionwhere andin which is an matrix of functionB continuous forin which is an matrix of functionscontinuous for 0≤S≤ t<∞.According to the decomposition theory of large scale system and with the help of Liapunovfunctional, we give a criterion for concluding that the zero solution of (2) (i.e. large scale system(1)) is uniformly asymptotically stable.We also discuss the large scale system with the decompositionand give a criterion for determining that the solutions of (4) (i.e. large scale system (3)) areuniformly bounded and uniformly ultimately bounded.Those criteria are of simple forms, easily checked and applied.

NONOVERLAPPING DOMAIN DECOMPOSITION METHOD WITH MIXED ELEMENT FOR ELLIPTIC PROBLEMS

In this paper we consider the nonoverlapping domain decomposition method based on mixed element approximation for elliptic problems in two dimentional space. We give a kind of discrete domain decomposition iterative algorithm using mixed finite element, the subdomain problems of which can be implemented parallelly. We also give the existence, uniqueness and convergence of the approximate solution.

Revisiting the Meaning of Requirements

Understanding the meaning of requirements can help elicit the real world requirements and refine their specifications. But what do the requirements of a desired software mean is not a well-explained question yet though there are many software development methods available. This paper suggests that the meaning of requirements could be depicted by the will-to-be environments of the desired software, and the optative interactions of the software with its environments as well as the causal relationships among these interactions. This paper also emphasizes the necessity of distinguishing the external manifestation from the internal structure of each system component during the process of requirements decomposition and refinement. Several decomposition strategies have been given to support the continuous decomposition. The external manifestation and the internal structure of the system component have been defined. The roles of the knowledge about the environments have been explicitly described. A simple but meaningful example embedded in the paper illustrates the main ideas as well as how to conduct the requirements decomposition and refinement by using these proposed strategies.