一种改进的基于形态骨架的二值图象编码

基于图象形态学的二值图象编码方法,近来在国际上得到了比较多的研究。为了提高基于骨架的编码方法效率,提出了一种基于形态骨架的子集--终极腐蚀（ultimate erosion）二值图象编码方法。该方法是基于扩展的非骨架点判定定理,使得有更多的点在编码过程中被判为非骨架点,从而提高了编码效率。与其他同类方法相比,这一方法更充分地去除了图象形态分析中的信息冗余,从而得到了很好的压缩效果,其对二值图象“工具”的压缩率达到0.065,大大优于游程码、四分树、链码等方法。     

基于Bayes定理的分类规则研究

研究了利用Bayes定理发现分类规则的方法,用Bayes定理可以发现分类规则,然后用分类规则进行数据分类。结合实例针对概念性数据集及包含数值性属性和概念性属性的数据集两种情况进行讨论。通过实例说明Bayes定理是数据挖掘中一种有效的数据分类方法。     

P-集合与信息F-伪装-辩识

P-集合（packet sets）是一个集合对,它由内P-集合（internal packet sets）与外P-集合（outer packet sets）共同构成。P-集合具有动态性,利用内P-集合,给出F-信息伪装与F-信息伪装生成概念;提出F-信息伪装度量定理与信息伪装被恢复-还原定理;给出辨识准则与方法。利用这些结果,给出F-信息伪装被恢复-还原的应用。P-集合是研究动态信息系统的一个新理论和新方法。     

命题时态逻辑定理证明新方法

本文通过对近１０年命题时态逻辑定理证明方法的研究，提出了一种新的证明方法，前人的工作基于对公式的现时部分和后时部分的分解，本文的工作是基于语义反驳树构造。这种新方法为计算机自动证明命题时态逻辑定理，提供了比较好的理论框架．最后还证明了该方法的可靠性和完全性．     

浅谈解的存在唯一性定理在《偏微分方程数值解》中的应用

从一个新的角度讨论常微分方程中解的存在唯一性定理在偏微分方程数值解法中的重要应用。给出一类伪双曲型偏微分方程的新的分裂混合有限元数值格式,将该格式转化成常微分方程系统,利用解的存在唯一性定理证明该系统是存在唯一解的。通过简短的讨论、概述明确解的存在唯一定理在偏微分方程数值解中的应用方法．并希望能够在教学科研未来的发展中有新的观念。     

一种安全协议的形式化设计方法

本文以协议分析器为辅助工具,结合定理证明方法,给出一个安全协议形式化设计方法。该方法首先根据协议规范构造全信息项及冗余协议,使用定理证明保证冗余协议的安全性。对冗余协议利用安全性保持约简规则和随机约简规则进行约简,从而得到最优约简协议。该方法实现了安全协议的自动设计,具有良好的扩展性,可以根据需求和协议的发展增加设计规则和约简规则。     

一种新的基于扩展规则的定理证明算法

基于扩展规则的定理证明方法是一种与归结方法互补的新的定理证明方法,首先通过对扩展规则的深入研究,给出了扩展规则的一个重要性质,设计并实现了该性质的判定算法.此外,从理论上分析及证明了该判定算法的时问和空间复杂性.基于此,提出了一种新的基于扩展规则的定理证明算法NER,将判定子句集可满足性问题转化为一系列文字集合的包含问题,而非计数问题.实验结果表明,算法NER的执行效率较原有扩展规则算法IER和基于归结的有向归结算法DR有明显提高,有些问题可以提高两个数量级.     

Automatic inductive theorem proving using prolog

Although Prolog is a programming language based on techniques from theorem proving, its use as a base for a theorem prover has not been explored until recently (Stickel, 1984). In this paper, we introduce a Prolog-based deductive theorem proving method for proving theorems in a first-order inductive theory representable in Horn clauses. The method has the following characteristics:

• 1.It automatically partitions the domains over which the variables range into subdomains according to the manner in which the predicate symbols in the theorem are defined.
• 2.For each of the subdomains the prover returns a lemma. If the lemma is true, then the target theorem is true for this subdomain. The lemma could also be an induction hypothesis for the theorem.
• 3.The method does not explicitly use any inductive inference rule. The induction hypothesis, if needed for a certain subdomain, will sometimes be generated from a (limited) forward chaining mechanism in the prover and not from employing any particular inference rule.

In addition to the backward chaining and backtracking facilities of Prolog, our method introduces three new mechanism—skolemization by need, suspended evaluation, and limited forward chaining. These new mechanisms are simple enough to be easily implemented or even incorporated into Prolog. We describe how the theorem prover can be used to prove properties of Prolog programs by showing two simple examples.     

操作系统安全验证形式化分析框架

结合当前形式化验证方法的特点和操作系统安全模型情况,本文提出了这些方法在操作系统安全分析中的应用。结合传统定理证明方法的优势,将模型检验方法纳入形式化安全分析体系当中,并分别提出了在安全分析中的应用情况。将用定理证明用于从模型到规则的分析,模型检验从实现中抽取模型,用于从实现到规则的分析。     

Numerical validation for systems of absolute value equations

This paper establishes a numerical validation test for solutions of systems of absolute value equations based on the Poincaré–Miranda theorem. In this paper, the Moore–Kioustelidis theorem is generalized for nondifferential systems of absolute value equations. Numerical results are reported to show the efficiency of the new test method.     

Generalized quantum no-go theorems of pure states

Various results of the no-cloning theorem, no-deleting theorem and no-superposing theorem in quantum mechanics have been proved using the superposition principle and the linearity of quantum operations. In this paper, we investigate general transformations forbidden by quantum mechanics in order to unify these theorems. First, we prove that any useful information cannot be created from an unknown pure state which is randomly chosen from a Hilbert space according to the Harr measure. And then, we propose a unified no-go theorem based on a generalized no-superposing result. The new theorem includes the no-cloning theorem, no-anticloning theorem, no-partial-erasure theorem, no-splitting theorem, no-superposing theorem or no-encoding theorem as a special case. Moreover, it implies various new results. Third, we extend the new theorem into another form that includes the no-deleting theorem as a special case.     

Improvements on the uncorrelated optimal discriminant vectors

The algorithm and the theorem of uncorrelated optimal discriminant vectors (UODV) were proposed by Jin. In this paper, we present new improvements to Jin's method, which include an improved approach for the original algorithm and a generalized theorem for UODV. Experimental results prove that our approach is superior to the original in the recognition rate.     

基于三层组织模型的一种Web服务组合策略

在研究Web服务三层组织模型和有限状态自动机的基础上,提出了一种新的Web服务组合策略,给出了一个服务的可组合性定理,并证明了定理的正确性。该策略以Web服务三层组织模型为基础,简化了BPEL中基于有限状态自动机的Web服务自动组合,精简了服务组合流程。最后对这种新的组合策略的优缺点作了分析。     

Numerical solution of hybrid fuzzy differential equation IVPs by a characterization theorem

In this paper, we study hybrid fuzzy differential equation initial value problems (IVPs). We consider the problem of finding their numerical solutions by using a recent characterization theorem of Bede for fuzzy differential equations. We prove a corollary to Bede’s characterization theorem and give a characterization theorem for hybrid fuzzy differential equation IVPs. Then we prove that any suitable numerical method for ODEs can be applied piecewise to numerically solve hybrid fuzzy differential equation IVPs. Numerical examples are provided which connect the new results with previous findings.     

A stability theorem of the direct Lyapunov's method for neutral-type systems in a critical case

A new stability theorem of the direct Lyapunov's method is proposed for neutral-type systems. The main contribution of the proposed theorem is to remove the condition that the 𝒟 operator is stable. In order to demonstrate the effectiveness, the proposed theorem is used to determine the stability of a neutral-type system in a critical case, i.e. the dominant eigenvalues of the principal neutral term (matrix D in Introduction) lie on the unit circle. This is difficult or infeasible in previous studies.     

A New Method for the Boolean Ring Based Theorem Proving

A new method for first-order theorem proving based on the Boolean ring approach is proposed. The method is an extension of Hsiang's N-Strategy in two aspects: (1) When the input polynomials are derived from clauses, our method is reduced to a more restricted (but still complete) version of N-Strategy: Only maximal atoms in an N-rule are considered for generating new inferences. (2) When the input polynomials are derived from non-clausal formulas, no new inference rules are needed in our method for ensuring the completeness. Unlike Kapur and Narendran's method which considers every pair of polynomials for superposition, our method restricts the pairs to those one of which consists of an odd number of monomials. The completeness proof of our method with the integration of reduction is also provided and is done by using the technique of semantic trees. The same technique is used to prove the completeness of N-strategy with reduction (using only N-rules and P-rules) for clausal theorem proving, thus it settles a longtime open problem.     

Hopf bifurcation via Volterra series

The Hopf bifurcation theorem gives a method of predicting oscillations which appear in a nonlinear system when a parameter is varied. There are many different ways of proving the theorem and of using its results, but the way which is probably the most useful, to control and system theorists, uses Nyquist loci in much the same way as the describing function method does. The main advantages of this method are dimensionality reduction, which eases the calculation, and the ability to cope with higher-order approximations than are used in the original Hopf theorem. This paper shows how such an approach to the Hopf bifurcation follows naturally and easily from Volterra series methods. Such use of Volterra series in nonlinear oscillations appears to be new. In many problems, the calculations involved are simplified when the Volterra series approach is taken, so the approach has practical merits as well as theoretical ones.     

Case studies of Z-module reasoning: Proving benchmark theorems from ring theory

A new method, called Z-module reasoning, was formulated for proving and discovering theorems from ring theory. In a case study, the ZMR system designed to implement this method was used to prove the benchmark x ³ ring theorem from associative ring theory. The system proved the theorem quite efficiently. The system was then used to prove the x ⁴ ring theorem from associative ring theory. Again, a proof was produced easily. These proofs, together with the successes in proving other difficult theorems from ring theory suggest that the Z-module reasoning method is useful for solving a class of problems relying on equality reasoning. This paper illustrates the Z-module reasoning method, and analyzes the computer proof of the x ³ ring theorem.This reasearch was supported in part by the Applied Mathematical Sciences subprogram of the office of Energy Research, U.S. Department of Energy, under contract W-31-109-Eng-38.     

Theorem Proving Based on the Extension Rule

Methods based on resolution have been widely used for theorem proving since it was proposed. This paper presents a new method for theorem proving that uses the inverse of resolution and employs the inclusion-exclusion principle to circumvent the problem of space complexity. We prove its soundness and completeness. The concept of complementary factor is introduced to estimate its complexity. We also show that our method outperforms resolution-based methods in some cases. Thus it is potentially a complementary method to resolution-based methods. This revised version was published online in August 2006 with corrections to the Cover Date.