Program state optimal method based on variable symbolic relation analysis

Program analysis is the prime method to program property analysis,which is widely used in the domain of parameter dependent relation,path coverage and test case generation,and a lot of progress has been made.Current program analysis is based on the method of symbolic execution,but symbolic execution is usually tackled with the problems of logic expression generation of path condition and low efficiency of constrain solver,which will affect the results of program analysis.Aiming at enhancing the path analysis efficiency,the path conditions of different paths were collected,the common symbolic expression was extracted and the efficiency of symbolic analysis was enhanced,then the logic expression set was generated,the dependent relation algorithm was used to enhance the efficiency of symbolic analysis.Experimental results demonstrate that the proposed method has the advantages of accurate time complexity and better analysis efficiency compare to traditional program analysis method.     

On Reliability Evaluation by Network Decomposition

A simple algorithm for evaluating the symbolic terminal-pair reliability of a complex system is presented. The system graph is decomposed into two subgraphs through a minimal cut. The system success is expressed in terms of certain successes of these subgraphs, and then changed into an equivalent disjoint expression which is directly converted on a one-to-one basis into a reliability expression. It yields unusually simple reliability expressions. The algorithm can be computerized but has not been done. Three examples illustrate the algorithm and compare it with other algorithms.     

网络系统可靠度的BDD算法

文中研究3-状态设备网络系统2-终端可靠度的计算问题。BDD是布尔函数的图形表示形式。武小悦和沙基昌提出了一个采用BDD方法求2-状态网络系统的不交化最小路集,从而直接计算网络系统可靠度的算法。通过引入简化技术,结合归约公式和BDD技术,给出了一个计算3-状态设备网络2-终端可靠度的一个新算法;算法有效地消除了冗余项,并且产生的分枝树具有结点少,可有效得到可靠度符号表达式。     

Efficient symbolic computation of approximated small-signalcharacteristics of analog integrated circuits

A symbolic analysis tool is presented that generates simplified symbolic expressions for the small-signal characteristics of large analog integrated circuits. The expressions are approximated while they are computed, so that only those terms are generated which remain in the final expression. This principle causes drastic savings in CPU time and memory, compared with previous symbolic analysis tools. In this way, the maximum size of circuits that can be analyzed, is largely increased. By taking into account a range for the value of a circuit parameter rather than one single number, the generated expressions are also more generally valid. Mismatch handling is explicitly taken into account in the algorithm. The capabilities of the new tool are illustrated with several experimental results     

Algorithm for efficient symbolic analysis of large analoguecircuits

An algorithm is presented that generates simplified symbolic expressions for the small-signal characteristics of large analogue circuits. The expressions are approximated while they are computed, so that only the most significant terms are generated which remain in the final expression. This principle leads to dramatic savings in CPU time and memory compared to existing techniques, significantly increasing the maximum size of circuits that can be analysed. By taking into account a range for the value of a circuit parameter rather than one single number the generated symbolic expressions are also generally valid     

一个符号神经网络的学习算法

本文首先根据神经科学和认知科学的研究，提出了一种符号神经网络结构，该结构溶符号机制和神经网络于一体，然后在此基础上研究了其学习算法，该算法结合神经网络ＢＰ学习算法和符号机制中学习算法的特点；最后通过实验，证实该算法的可行性和先进性。     

Two-stage fuzzy inference system for symbolic simplification of analog circuits

This paper presents a knowledge-based fuzzy approach to symbolic circuit simplification in an effort to imitate human reasoning and knowledge of circuit designer experts. The fuzzy approach differs from the conventional simplification techniques in that it can efficiently combine different input variables to obtain optimal simplified expressions. Additionally, this method was chosen due to its adjustability and interpretability, as well as its ability to manage very complex symbolic expressions. The proposed algorithm uses fuzzy logic to simplify the symbolic circuit transfer functions in two stages. In the first stage, a fuzzy system is applied to directly eliminate nonessential circuit components, resulting simplified circuit topology which also yields simpler transfer function. In the second stage, another fuzzy system is used to further simplify the symbolic transfer function from the already simplified circuit, such that deeper insight into the circuit behavior can be obtained. Symbolic and numerical results show that the fuzzy approach outperforms the conventional techniques in terms of accuracy, expression complexity, and CPU running time.     

New Topological Formula and Rapid Algorithm for Reliability Analysis of Complex Networks

Part I derives a new topological formula for the terminalpair reliability of complex networks. The formula generates only non-cancelling terms. The non-cancelling terms in the reliability expression correspond one-to-one with the acyclic subgraphs of the given probabilistic graph. Part II introduces the concept of neutral sequences in acyclic graphs; several of their important properties are established. Based on these results a powerful algorithm for generating the reliability expression is presented. The reliability expression is obtained in symbolic factored form. Examples indicate that the present algorithm is appreciably faster than earlier methods. The properties of cyclic and acyclic graphs established in this paper are significant new results in the theory of digraphs and have further ramifications and wider application than in reliability.     

A comparison of algorithms for terminal-pair reliability

Four algorithms for the terminal-pair-reliability problem are compared. Nelson (1970), Lin (1976), Shooman (1968), and Dotson (1979) algorithms are used in this study. It is shown that the Dotson algorithm is the fastest among the terminal-pair reliability algorithms analyzed. The Dotson algorithm is suited not only for numerical reliability, but for obtaining symbolic expression for the terminal-pair reliability with no additional effort. By modifying the Dotson algorithm the efficiency can be further improved. The modifications to this algorithm are listed and the reliability of the modified Dotson algorithm is computed     

Variation range based simplification for meaningful symbolic analysis of analog integrated circuits

This paper presents a variation range based symbolic simplification technique, where each circuit parameter is represented via a range of variation. We generate a database to handle the variation ranges of the circuit parameters and perform simulated annealing algorithm to achieve the most compact symbolic expressions. In contrast to the existing techniques, the main advantage of the proposed method is that the simplified symbolic expressions have an acceptable generalizability in the whole ranges of variations of the circuit parameters. The maximum allowable simplification error can be controlled by the user based on the required accuracy level that he needs. Simulation results demonstrate that the proposed method outperforms the conventional techniques in terms of expression complexity, accuracy and generalizability of the simplified expressions. The resultant expressions are only as complicated as necessary to give the required accuracy in the results, which help in giving a better insight into the circuit behavior.     

非对称X-演算的符号互模拟验证算法

非对称x-演算是一种移动计算模型。文介绍非对称x-演算的语法和符号操作语义，给出非对称x-演算的符号互模拟的验证算法，该算法根据算法输出的谓词等式系，求解最大符号解。并证明算法正确性．这在一定程度上为今后的自动机验证提供了理论基础。     

Recursive enumeration of state graphs for the reliability evaluation of logic circuits

A method is presented for the recursive enumeration of State Graphs in a given Circuit Equivalent Graph [1] for logic circuit reliability evaluation purposes. This enumeration is quite complicated and requires the systematic searching through the Circuit Equivalent Graph. The enumeration is accomplished by symbolic notation, which is a powerful tool for denoting State Graphs. The state-graph expression in symbolic form (SG-expression) is a string of literals and arc symbols and maps uniquely a given State Graph. Using a Last-In-First-Out manipulation approach and assuming appropriate rules for the ordering of State Graphs, an enumeration algorithm is developed which satisfies two important objectives; namely, the total enumeration of SG-expressions from a Circuit Equivalent Graph and the recursive searching of SG-expressions which correspond to a given cube of terminal states.     

网络最大流问题的一种新的符号ADD求解算法

通过对网络及网络最大流问题的符号代数判定图描述,在Trff算法的基础上,给出了网络最大流问题的一种新的符号ADD求解算法。与Dinic、Karzanov算法相比,本文算法的空间复杂度较低。实验结果表明,该算法可处理更大规模的问题。     

一种计算符号系数矩阵行列式值的快速算法

在模拟电路符号网络函数分析的代数法中，矩阵行列式的计算直接关系到符号分析程序的效率。在置换法和展开法的基础上，提出了一种新的计算符号行列式值的两端收缩算法，并在符号分析程序中实现，还给出了与该算法有关的数据结构，以及几种算法与比较结果。     

A new algorithm for computing the reliability of complex networks by the cut method

It is well known that computing network reliability is equivalent to computing network unreliability. A fusion of the reliability branching algorithm (RBA) with the path method has given a new method for symbolic reliability analysis. The present paper gives a new method for symbolic unreliability; it is a combination of the RBA with the cut method. The algorithm is simple for computing by hand and has easy execution for the use of computers.     

On the computation of weight enumerators for convolutional codes

Performance bounds for maximum-likelihood decoding of convolutional codes over memoryless channels are commonly measured using the distance weight enumerator T(x,y), also referred to as the transfer function, of the code. This paper presents an efficient iterative method to obtain T(x,y) called the state reduction algorithm. The algorithm is a systematic technique to simplify signal flow graphs that algebraically manipulate the symbolic adjacency matrix associated with the convolutional code. Next, the algorithm is modified to compute the first few terms of the series expansion of T(1,y) and {/spl part/T(x,y)//spl part/x}/sub x=1/ (the distance spectra) without first computing the complete T(x,y).     

Calculation of node-pair reliability in large networks withunreliable nodes

A new efficient method that compensates for unreliable nodes in network reliability computations is presented. This method can be embedded in the modified Dotson algorithm or any algorithm that generates a symbolic reliability expression for networks with perfect nodes. Its cost increases linearly with the number of links, and the effect of unreliable nodes can be directly computed. This method supplants the Aggarwal method and other methods of compensating for unreliable nodes in the calculation of node-pair reliability. When combined with the modified Dotson algorithm, this method provides accurate reliability estimates for networks so large that the Theologou-Carlier algorithm cannot complete its computations in a reasonable amount of time. For such networks, the new method can be embedded in the modified Dotson algorithm to estimate both the node-pair reliability and the error in this estimate even if the algorithm is terminated before completion     

Computerization of the R-ABC algorithm

The R-ABC algorithm is a simple algorithm for evaluating the symbolic terminal-pair reliability of a complex system. However, this algorithm is not computerized. This paper tries to computerize the R-ABC algorithm.     

Fiber spot size: a simple method of calculation

The ability to integrate the Laguerre-Gauss functions in closed form is exploited to allow a simple but accurate evaluation of single-mode fiber spot size using Galerkin's method. The method avoids the need for numerical integration in a broad class of refractive-index profiles. Its simplicity depends on the use of a pattern-matching algorithm to avoid the numerical integration normally called for. The algorithm is very fast and gives exact results. The development of symbolic computer languages makes this approach especially easy. A symbolic program was used to predict the spot size and the far-field radiation pattern, and the results are compared with the exact values, getting excellent results     

A New Algorithm for Symbolic System Reliability Analysis

This paper presents a new algorithm for symbolic system reliability analysis. The method is applicable to system graphs with unreliable branches or nodes. Each branch is directed or undirected. Element probabilities need not be equal, but their failures are assumed to be s-independent. The new method makes no attempt to generate mutually exclusive events from the set of paths or cutsets but uses a technique to reduce greatly the number of terms in the reliability expression. Actual programming results show that the new method can efficiently handle systems having fewer than 20 paths or cutsets between the input-output node pair.