Pi+演算及其对Petri网的表达

为了研究Pi演算模型的表达能力,作者用它来表达Petri网系统,证明了Petri网的某些子类,如自由选择网等,可以直接用Pi演算表达.然而对于一般的Petri网,表达却遇到了困难.文中提出了一种对Pi演算的扩展,称为Pi+演算,在原有Pi演算的通信机制中增加了多原语同步通信机制.证明了所有一般Petri网系统均可以用P...     

复杂分支和同步模式的Pi演算描述

Pi演算是一种描述和分析动态并发系统的计算模型。对Pi演算进行研究后,提出了以Pi演算作为工作流形式化的基础,并利用Pi演算对复杂分支和同步工作流模式进行了详细的描述。     

k-选择网和Pi演算的表达能力

文中定义了Petri网的一子类系列:k-选择网,它形成一个后类包含前类的Petri网子类的无穷序列,证明了此无穷序列的并集等于Petri网类,自由选择网是k=1的k-选择网,即1-选择网.在证明自由选择网系统可以用Pi演算表达的基础上,文中进一步证明了所有2-选择网系统可以用Pi演算表达.     

Pi演算与动态描述逻辑DDL的关系研究

分析了Pi演算与动态描述逻辑DDL之间的关系:DDL分别从静态结构与动态结构两方面对Pi演算的若干过程定义进行描述,体现了过程的逻辑结构及过程间逻辑关系的变化;以一种基于Pi演算的过程模型为基础,分析了ALC描述逻辑、TBox和ABox的语义,并通过一个例子说明Pi演算对DDL动态知识的变化过程的描述.以上工作表明:DDL的可判定推理可解决基于Pi演算的动态系统的某些一致性检测问题,而Pi演算对动态系统的描述能力可解决DDL动态知识的变化过程的描述问题.     

基于Pi验算的信息化系统流程研究与设计

软件建模是把现实世界的需求抽象成概念模型,软件编码是把概念模型转变成能够运行的代码,在建模阶段,针对传统的UML即统一建模语言对信息系统业务流程的建模,无法严谨地定义和模拟信息系统的业务流程,不能保证流程本身的正确性和一致性等问题.以物流订单流程为例,研究BPMN表达业务流程及与形式化语言之间的转换,用形式化描述语言Pi演算描述和验证BPMN已描述的信息系统业务流程,通过JPDL直接定义出已通过Pi演算验证的订单流程,并应用于工作流引擎JBPM中,从而保证应用系统业务流程的正确性.     

基于Pi演算的BPMN编排模式

针对业务流程建模标记（BPMN）无法依靠自身对编排进行形式化分析的问题,提出用Pi演算描述BPMN编排模式,实现对BPMN编排的描述。BPMN编排模式是服务交互模式的BPMN表达。实验结果表明,该方法能够找到并排除BPMN编排中的死锁。     

软件实体中预期协作路径的获取方法

为解决软件实体间的预期协作路径获取问题,提出一种软件实体中预期协作路径的获取方法。结合UML与Pi演算理论,在对软件实体行为分析的基础上,对实体行为进行Pi演算语义抽取,利用Pi演算的操作语义推演实体协作,生成实体预期协作路径集,并以可扩展标记语言方式对其进行存储。应用结果表明,该方法能支持软件实体预期协作路径的获取,为可信软件研究中软件预期行为获取方法提供有益补充。     

基于Pi演算的OWl-s的Web服务的自动组合

Web服务组合研究领域的一个重要的问题是如何形式化描述Web服务组合,如何验证服务组合的正确性。Web服务组合的形式化模型可以用来检查、验证Web服务组合以保证组合的正确性。针对目前最主要的一种语义Web服务组合的规范WEB本体论语言(Ontology Web Langage-Semantic,简称OWL-S),给出基于Pi演算的形式化描述,定义了Pi演算和OWl-S之间的概念映射,并给出了OWl-S的基于Pi演算的形式化模型,最后通过一个案例给出了模型验证的方法。     

使用Pi演算的构件交互可信性验证模型

为验证基于构件的软件系统中构件间交互的可信性,将统一建模语言(unified modeling language,UML)与Pi演算理论相结合,提出了一个软件构件间交互的可信性验证模型。在构件行为分析的基础上,利用抽取规则抽取Pi演算语义来描述构件的行为。进一步利用Pi演算的操作语义推演构件间的实际交互行为。将得到的实际交互行为与预期交互行为比对,可判断构件交互的可信性。最后,通过实例对该模型的具体应用进行了阐述。该模型能够对基于构件的软件系统中任意两个相互交互的构件之间交互的可信性进行验证,为判断该类系统中构件间交互的可信性提供了有效方法。     

SQL查询到扩充的元组关系表达式变换

SOL是标准的关系数据库查询语言,本文在关系代数和元组演算的基础上,定义了一种扩充的元组关系表达式,它能表达SOL 的聚集函数、分组运算、嵌套子查询。将SQL 变换为扩充的元组关系表达式,使我们可以用扩充的元组关系表达式来研究SQL 的语义和查询优化。     

On the expressiveness and decidability of higher-order process calculi

In higher-order process calculi, the values exchanged in communications may contain processes. A core calculus of higher-order concurrency is studied; it has only the operators necessary to express higher-order communications: input prefix, process output, and parallel composition. By exhibiting a deterministic encoding of Minsky machines, the calculus is shown to be Turing complete. Therefore its termination problem is undecidable. Strong bisimilarity, however, is shown to be decidable. Furthermore, the main forms of strong bisimilarity for higher-order processes (higher-order bisimilarity, context bisimilarity, normal bisimilarity, barbed congruence) coincide. They also coincide with their asynchronous versions. A sound and complete axiomatization of bisimilarity is given. Finally, bisimilarity is shown to become undecidable if at least four static (i.e., top-level) restrictions are added to the calculus.     

Complexity results for classes of quantificational formulas

We analyze the computational complexity of determining whether F is satisfiable when F is a formula of the classical predicate calculus obeying certain syntactic restrictions. For example, for the monadic predicate calculus and the Gödel or 3 … ???? … 3 prefix class we obtain lower and upper nondeterministic time bounds of the form c^{n/log n}. The lower bounds are established by using acceptance problems for time-bounded Turing machines and alternating pushdown and stack automata.     

Logically Possible Machines

I use modal logic and transfinite set-theory to define metaphysical foundations for a general theory of computation. A possible universe is a certain kind of situation; a situation is a set of facts. An algorithm is a certain kind of inductively defined property. A machine is a series of situations that instantiates an algorithm in a certain way. There are finite as well as transfinite algorithms and machines of any degree of complexity (e.g., Turing and super-Turing machines and more). There are physically and metaphysically possible machines. There is an iterative hierarchy of logically possible machines in the iterative hierarchy of sets. Some algorithms are such that machines that instantiate them are minds. So there is an iterative hierarchy of finitely and transfinitely complex minds.     

Interactive foundations of computing

The claim that interactive systems have richer behavior than algorithms is surprisingly easy to prove. Turing machines cannot model interaction machines (which extend Turing machines with interactive input/output) because interaction is not expressible by a finite initial input string. Interaction machines extend the Chomsky hierarchy, are modeled by interaction grammars, and precisely capture fuzzy concepts like open systems and empirical computer science. Computable functions cannot model real-world behavior because functions are too strong an abstraction, sacrificing the ability to model time and other real-world properties to realize formal tractability.Part I of this paper examines extensions to interactive models for algorithms, machines, grammars, and semantics, while Part II considers the expressiveness of different forms of interaction. Interactive identity machines are already more powerful than Turing machines, while noninteractive parallelism and distribution are algorithmic. The extension of Turing to interaction machines parallels that of the lambda to the pi calculus. Asynchronous and nonserializable interaction are shown to be more expressive than sequential interaction (multiple streams are more expressive than a single stream).In Part III, it is shown that interaction machines cannot be described by sound and complete first-order logics (a form of Godel incompleteness), and that incompleteness is inherently necessary to realize greater expressiveness. In the final section the robustness of interactive models in expressing open systems, programming in the large, graphical user interfaces, and agent-oriented artificial intelligence is compared to the robustness of Turing machines. Less technical discussion of these ideas may be found in [25–27]. Applications of interactive models to coordination, objects and components, patterns and frameworks, software engineering, and AI are examined elsewhere [28,29].The propositions P1-P36 embody the principal claims, while observations 01 through 040 provide additional insights.     

On parallel Turing machines with multi-head control units

This paper deals with parallel Turing machines with multi-head control units on one or more tapes which can be considered as a generalization of cellular automata. We discuss the problem of finding an appropriate measure of space complexity. A definition is suggested which implies that the model is in the first machine class. It is shown that without loss of generality it suffices to consider only parallel Turing machines of certain normal forms.     

Accelerating Turing Machines

Minds and Machines - Accelerating Turing machines are Turing machines of a sort able to perform tasks that are commonly regarded as impossible for Turing machines. For example, they can determine...     

From Symbol to ‘Symbol’, to Abstract Symbol: Response to Copeland and Shagrir on Turing-Machine Realism Versus Turing-Machine Purism

In their recent paper “Do Accelerating Turing Machines Compute the Uncomputable?” Copeland and Shagrir (Minds Mach 21:221–239, 2011) draw a distinction between a purist conception of Turing machines, according to which these machines are purely abstract, and Turing machine realism according to which Turing machines are spatio-temporal and causal “notional" machines. In the present response to that paper we concede the realistic aspects of Turing’s own presentation of his machines, pointed out by Copeland and Shagrir, but argue that Turing's treatment of symbols in the course of that presentation opens the door for later purist conceptions. Also, we argue that a purist conception of Turing machines (as well as other computational models) plays an important role not only in the analysis of the computational properties of Turing machines, but also in the philosophical debates over the nature of their realization.     

Theory of one-tape linear-time Turing machines

A theory of one-tape two-way one-head off-line linear-time Turing machines is essentially different from its polynomial-time counterpart since these machines are closely related to finite state automata. This paper discusses structural-complexity issues of one-tape Turing machines of various types (deterministic, nondeterministic, reversible, alternating, probabilistic, counting, and quantum Turing machines) that halt in linear time, where the running time of a machine is defined as the length of any longest computation path. We explore structural properties of one-tape linear-time Turing machines and clarify how the machines’ resources affect their computational patterns and power.     

基于量子逻辑的图灵机及其通用性

基于量子逻辑的自动机理论是量子计算模型的一个重要研究方向.该文研究了基于量子逻辑的图灵机(简称量子图灵机)及其一些变形,给出了包括非确定型量子图灵机l-VTM,确定型量子图灵机l-VDTM以及相应类型的多带量子图灵机,并引入量子图灵机基于深度优先与宽度优先识别语言的两种不同定义方式,证明了这两种定义方式在量子逻辑意义下是不等价的.进一步证明了l-VTM、l-VDTM与相应类型的多带量子图灵机之间的等价性.其次,给出了量子递归可枚举语言及量子递归语言的定义,并给出了二者的层次刻画,证明了l-VTM与l-VDTM不等价,但两者作为量子递归语言的识别器是等价的.最后,文中讨论了基于量子逻辑的通用图灵机的存在性问题,给出了一套合理编码系统,证明了基于量子逻辑的通用图灵机在其所取值的正交模格无限时不存在,而在其所取值的正交模格有限时是存在的.     

The complexity of small universal Turing machines: A survey

We survey some work concerned with small universal Turing machines, cellular automata, tag systems, and other simple models of computation. For example, it has been an open question for some time as to whether the smallest known universal Turing machines of Minsky, Rogozhin, Baiocchi and Kudlek are efficient (polynomial time) simulators of Turing machines. These are some of the most intuitively simple computational devices and previously the best known simulations were exponentially slow. We discuss recent work that shows that these machines are indeed efficient simulators. As a related result, we also find that Rule 110, a well-known elementary cellular automaton, is also efficiently universal. We also review a large number of old and new universal program size results, including new small universal Turing machines and new weakly, and semi-weakly, universal Turing machines. We then discuss some ideas for future work arising out of these, and other, results.