W（a, b） Lie Conformal Algebra and Its Conformal Module of Rank One

For any complex parameters a, b, let W（a, b） be the Lie algebra with basis {Li, Hi｜i ∈ Z} and relations [Li,Lj] = （j - i）Li＋j, [Li,Hj] = （a ＋ j ＋ bi）Hi＋j and [Hi, Hi] = 0. In this paper, we construct the W（a, b） conformal algebra for some a, b and its conformal module of rank one.

Formal Inferring the Law of Conservation of Energy from Assuming A-Priori-ness of Knowledge in a Formal Axiomatic Epistemology System Sigma

The research purpose is invention (construction) of a formal logical inference of the Law of Conservation of Energy within a logically formalized axiomatic epistemology-and-axiology theory Sigma from a precisely defined assumption of a-priori-ness of knowledge. For realizing this aim, the following work has been done: 1) a two-valued algebraic system of formal axiology has been defined precisely and applied to proper-philosophy of physics, namely, to an almost unknown (not-recognized) formal-axiological aspect of the physical law of conservation of energy;2) the formal axiomatic epistemology-and-axiology theory Sigma has been defined precisely and applied to proper-physics for realizing the above-indicated purpose. Thus, a discrete mathematical model of relationship between philosophy of physics and universal epistemology united with formal axiology has been constructed. Results: 1) By accurate computing relevant compositions of evaluation-functions within the discrete mathematical model, it is demonstrated that a formal-axiological analog of the great conservation law of proper physics is a formal-axiological law of two-valued algebra of metaphysics. (A precise algorithmic definition of the unhabitual (not-well-known) notion “formal-axiological law of algebra of metaphysics” is given.) 2) The hitherto never published significantly new nontrivial scientific result of investigation presented in this article is a formal logical inference of the law of conservation of energy within the formal axiomatic theory Sigma from conjunction of the formal-axiological analog of the law of conservation of energy and the assumption of a-priori-ness of knowledge.

Formally Deriving the Third Newton’s Law from a Pair of Nontrivial Assumptions in a Formal Axiomatic Theory “Sigma-V”

The article is devoted to hitherto never undertaken applying an almost unknown logically formalized axiomatic epistemology-and-axiology system called “Sigma-V” to the Third Newton’s Law of mechanics. The author has continued investigating the extraordinary (paradigm-breaking) hypothesis of formal-axiological interpreting Newton’s mathematical principles of natural philosophy and, thus, has arrived to discrete mathematical modeling a system of formal axiology of nature by extracting and systematical studying its proper algebraic aspect. Along with the proper algebraic machinery, the axiomatic (hypothetic-deductive) method is exploited in this investigation systematically. The research results are the followings. 1) The Third Newton’s Law of mechanics has been modeled by a formal-axiological equation of two-valued algebraic system of metaphysics as formal axiology. (Precise defining the algebraic system is provided.) The formal-axiological equation has been established (and examined) in this algebraic system by accurate computing compositions of relevant evaluation-functions. Precise tabular definitions of the evaluation-functions are given. 2) The wonderful formula representing the Third Newton’s Law (in the relevant physical interpretation of the formal theory Sigma-V) has been derived logically in Sigma-V from the presumption of a-priori-ness of knowledge. A precise axiomatic definition of the nontrivial notion “a-priori-ness of knowledge” is given. The formal derivation is implemented in strict accordance with the rigor standard of D. Hilbert’s formalism;hence, checking the formal derivation submitted in this article is not a difficult task. With respect to proper theoretical physics, the formal inference is a nontrivial scientific novelty which has not been discussed and published elsewhere yet.

Verifying Monoid and Group Morphisms over Strongly Connected Algebraic Automata

Automata theory has played an important role in theoretical computer science since last couple of decades. The alge-braic automaton has emerged with several modern applications, for example, optimization of programs, design of model checkers, development of theorem provers because of having certain interesting properties and structures from algebraic theory of mathematics. Design of a complex system requires functionality and also needs to model its control behavior. Z notation has proved to be an effective tool for describing state space of a system and then defining operations over it. Consequently, an integration of algebraic automata and Z will be a useful computer tool which can be used for modeling of complex systems. In this paper, we have linked algebraic automata and Z defining a relationship between fundamentals of these approaches which is refinement of our previous work. At first, we have described strongly connected algebraic automata. Then homomorphism and its variants over strongly connected automata are specified. Next, monoid endomorphisms and group automorphisms are formalized. Finally, equivalence of endomorphisms and automorphisms under certain assumptions are described. The specification is analyzed and validated using Z/Eves toolset.

Formally Inferring Galileo Galilei Principle of Relativity of Motion in an Axiomatic System “Sigma+V” from a Triple of Nontrivial Assumptions

The present paper submits a result of applying a hitherto unknown logically formalized axiomatic axiology-and-epistemology theory “Sigma+V” to the relativity principle formulated by Galileo Galilei. By this application, the author has continued checking the remarkable (paradigm-breaking) hypothesis that formal-axiological interpreting strictly universal laws of classical theoretical mechanics could have a heuristic value for the theory proper. Along with systematical studying proper algebraic structure of formal axiology of nature, the axiomatic (hypothetic-deductive) method is used in this research as well. The investigation accomplishments are the followings. Galileo Galilei principle of relativity of motion has been represented in a two-valued algebraic system of formal axiology by a wonderful formal-axiological equation which could be called a “formal-axiological analog of Galileo relativity principle”. A precise definition of that algebraic system is given. The remarkable formal-axiological equation has been created (and checked) in that algebraic system by attentive computing relevant compositions of evaluation-functions. Precise definitions of the relevant evaluation-functions are accomplished by tables. The remarkable formula modeling Galileo Galilei principle of relativity of motion (given the appropriate interpretation of the formal theory) has been formally-logically inferred within Sigma+V from a couple of nontrivial assumptions, namely, 1) a precisely defined assumption of a-priori-ness of knowledge, 2) the above-mentioned formal-axiological analog of the relativity principle by Galileo Galilei. A not-manifest but quite exact axiomatic definition of “a-priori-ness of knowledge” is provided. The formal-logical inference is performed in perfect accordance with the mathematical rigor norms formulated within the formalism doctrine by D. Hilbert, therefore, examining the formal deductive inference submitted in the paper can be accomplished easily. Being a nontrivial scientific novelty for proper theoretical physics, hitherto the formal-logical derivation has not been published and discussed elsewhere.

基于进程代数的TCG远程证明协议的形式化验证

可信计算组织(Trusted Computing Group,TCG)的远程证明协议是最早提出的远程证明的解决方案,其协议的形式化验证对于工程实施具有重要意义.分析了TCG远程证明协议的两种形式——直接证明协议和借助可信第三方的证明协议,对它们进行了抽象处理,得到了两种协议形式的抽象模型.在抽象模型的基础上,给出了基于进程代数的形式化描述,并分别进行了形式化验证.验证结果表明两种协议形式的并行系统均展示了期望的外部行为.

格值命题逻辑系统L(X)(Ⅱ)

本文讨论以格蕴涵代数为真值域的格值命题逻辑系统Ｌ（Ｘ）的语法问题，给出了系统的公理和推演规则，并证明了系统的可靠性定理、演绎定理＊及协调性定理。

基于构造类别代数的数据流和控制流相结合的协议测试

如何从协议规范中生成即考虑控制流又兼顾数据流的测试用例是一个很有挑战的问题,本文提出了一种基于构造类别代数的数据流与控制流相结合的测试方法,给出了在其上的测试用例生成算法,有限状态机模型到构造类别代数模型的转换算法,并且给出了在一个实际的路由协议RIP的测试中的应用例子.

本体定义及本体代数

基于现有的本体定义,采用函数式描述语言精确定义了本体建模基元,给出一种新的本体形式化描述,并给出了本体间近义关联的定义,在新本体形式化描述和本体间近义关联定义的基础上,提出一种具有封闭性的本体代数定义,同时结合函数式描述语言,给出了其形式化描述.

基于进程代数安全协议验证的研究综述

安全协议用于实现开放互联网络的通信安全 ,进程代数是一类使用代数方法研究通信并发系统理论的泛称 ,基于进程代数的安全协议验证是以进程代数作为安全协议描述语言的安全协议形式化验证方法 描述了基于进程代数的安全协议验证研究的 4种主要方法 :基于踪迹语义的方法 ;基于互模拟验证的方法 ;基于类型理论的方法 ;基于逻辑程序的方法

可信计算中信任链建立的形式化验证

为了对可信平台控制模块的信任链建立过程进行理论验证,在对基于可信平台控制模块(trusted platform control module,TPCM)的信任链建立过程进行抽象处理的基础上,给出了抽象模型中各个实体状态的进程代数描述,并利用进程代数的公理系统做了形式化验证.验证的结果表明系统具有期望的外部行为.

密码协议的分层安全需求及验证

将密码协议的安全需求分为浅层需求和深层需求 2个层面 ,阐述了密码协议的分层安全需求 .采用近世代数和时序逻辑的方法定义了形式化描述语言 ,并形式化地描述了密码协议的分层安全需求 .将类BAN逻辑与模型检查相结合 ,在Abadi Tuttle模型的基础上建立密码协议的计算模型 .以Otway Rees协议为例 。

基于ε-互模拟的软件近似正确性模型

软件正确性是软件可信性的重要属性。在实际软件开发和设计中,需要不断地对软件进行修改,从而软件越来越正确。为了讨论软件的动态近似正确性,基于概率进程代数的ε-互模拟,建立软件越来越正确的形式化描述。定义ε-极限互模拟,用来反应软件实现与规范之间的关系,给出一些特殊的ε-极限互模拟。提出ε-互模拟极限,用其刻画规范是软件实现的极限形式,同时证明ε-互模拟极限的一些性质。

XML形式数据模型及其查询代数

提出了XML的形式教据模型及其查询代数,主要包括以下几个方面:构造先后序关系、引入带根连通有向 图、建立XML形式数据模型(XFDM)和XML查询代数(XFQA)。它形成了一个较为完整的XML数据库管理系统的 理论基础,可以作为XML以及其它半结构化数据库管理系统查询存储、查询分解、查询优化和查询实现的形式化基础。

基于进程代数的UML序列图的形式语义

UML序列图用于建模实例间动态交互过程.但UML规范并没有给出其形式化的动态语义,这不利于对模型进行形式化验证和证明。本文把序列图中的事件动作及其执行序列映射为进程代数中的进程表达式,利用进程代数语义框架来构建UML序列图的形式语义。首先,建立了序列图到进程代数的语义映射规则;然后用Plotkin风格的结构化操作语义给出并证明条件组合算子演绎规则;最后,归纳定义了算子次序约束条件并证明了其可终止性。

形式语言的代数模型研究

用统一的基础理论定义形式语言的基本概念是实现软件自动化的重要基石,试图用递归论的术语定义串、序列函词、串等价等程序语言中的基本概念,证明了任何上下文无关语言的串实例都与一个半格系统相对应,对自动化建立语言的代数语义模型做出了有益的尝试.

基于部分交互的软件近似度量模型

软件对环境的依赖性主要体现在软件与环境的交互。在实际中,有时软件与环境未必成功交互。其交互程度对软件的性能有着很大的影响。为测试不同软件在环境下的性能,需要对软件与环境的交互能力进行比较。在进程代数理论基础上,利用完整迹语义,建立软件近似程度的量化模型。形式化描述软件与环境的部分交互。列举一些例子对模型进行说明。建立软件近似程度的量化模型,证明一些代数性质。进一步,建立评价软件在与环境交互方面好坏的标准。

基于信息流控制的HDFS敏感数据安全增强

针对HDFS已有保护方法如认证授权、数据加密、访问控制和审计方法都不能保证敏感数据端到端的安全性,提出了一个用于HDFS的安全代数语言SALH(security algebra language for HDFS),给出了SALH的语义和语法;采用SALH形式化描述了HDFS信息流跟踪和控制模型并证明了模型的无干扰安全性。最后,给出了原型系统IF-HDFS设计与实现关键技术,原型系统的功能和性能测试结果表明IF-HDFS可实时、有效、准确地实现信息流跟踪与控制。

基于CCS的信号量形式化建模与验证

利用通信系统演算CCS(Calculus of Communicating Systems),对用来解决进程间通信问题的信号量给出了形式化建模和验证的方法,并利用该方法对以信号量机制解决生产者—消费者问题和哲学家进餐问题进行建模、逻辑说明和验证。该方法具有一定通用性,并可将其推广到其他通过信号量机制解决进程通信的问题当中。

数学、计算机与音乐

音乐中的科学问题正日益受到广泛重视 .它不仅是当今迅猛发展的多媒体研究领域的重要组成部分 ,而且反过来已成为“计算机科学形成过程中最重要的推动力之一”[1] .本文揭示了音乐艺术的部分科学特性及相应的研究思路 ,内容涉及数字音乐原理、MIDI文化现象、音乐艺术的形式化手段以及代数研究方法 .