高效率重写型程序的设计

本文考虑如何设计高效率(即重写步数较少的)重写型程序。文中以计算Fibonacci数列的程序为例．比较具有相同功能的重写型程序,展示编写高效率重写型程序的可能性。介绍利用动态项重写计算编写高效率重写型程序的直观、简洁的方法。其中．动态项重写计算是项重写系统的元计算模型,其计算同样基于项重写。     

项重写系统等价性的归纳证明

尽管学者们在计算机软件理论及相关数学理论方面做出了不懈的努力,但伴随着计算机硬件的高速发展而来的软件危机却日益严峻,其原因复杂多样。其中,主要原因之一是缺乏程序验证的方法和工具。程序设计的主要步骤有:描述问题、设计程序、实现程序及测试程序。需要注意的是,这里是测试程序的正确性而非证明程序的正确性,这样程序的正确性就不能从根     

项重写系统弱基终止性的归纳证明

1.引言项重写系统是一种受到广泛研究和应用的形式计算模型。一个项重写系统由一组称为重写规则的定向等式组成。例如,下面的R是一个由五个重写规则组成的、定义用({0,s})表示的自然数集N上的两倍函数d(x)=2×n:N→N的项重写系统:     

重叠规则与歧义性

重写系统是一种一般的计算模型，重写系统的归约策略的范式化性质对于实际应用重写系统进行计算具有决定意义，而重叠规则导致的歧义性是使归约过程复杂化重要原因，本文对重写系统的歧义性进行了初步研究，并对一类常见的歧义问题作了具体分析，同时提出了解决办法。     

项重写系统的并行实现方案

项重写系统的并行归约可以提高归约的效率，在无共享内存的Ｔｒａｎｓｐｕｔｅｒ网络上实现时要考虑任务的分配，项的拼装，归约任务的控制等问题，其中怎么样减少机间的机内进程的通信慢提高系统效果的关键。本文从控制方式角度讨论在不同拓扑结构的Ｔｒａｎｓｐｕｔｅｒ网络上实现项重写系统的方案，重点介绍基于树形结构下的控制方法，进程安排和通讯形式。     

重写系统的模块分解

Ｍｉｄｄｅｌｄｏｒｐ和Ｔｏｙａｍａ证明，强加构造原则到项重写系统可获得完备概念的模块性，并且系统分解成的各部分间可共亨函数符号和重量写规则。本文推广他们的结论，当构造性的项重写系统引用定义在其它系统中的函数符号时，完备概念的模块性仍保持。该结论对代数规范和基于项重写的编程语言等方面是很有意义的。     

TA4SP的认证性扩展

认证性是安全协议检测的重要特性之一,但TA4SP自动协议证明器无法对安全协议的认证性进行检测。针对该问题,提出一种TA4SP的认证性检测方法。该方法基于对TA4SP设计原理的分析,采用分层认证思想,实现对其认证性的理论扩展,其结构清晰、易于形式化。实例表明,通过该方法改进后的TA4SP能有效检测安全协议的认证性。     

Knuth－Bendix过程的发散现象的研究

Ｋｎｕｔｈ－Ｂｅｎｄｉｘ完备过程不终止的起因研究得很少．本文研究引起不终止的重写规则的结构性质，提出了相容交叉规则对的概念，推广了文献［６］的结论，并提出了为构造系统检验该过程是否不终止的方法．     

重叠规则与歧义性*

重写系统是一种一般的计算模型．重写系统的归约策略的范式化性质对于实际应用重写系统进行计算具有决定意义，而重叠规则导致的歧义性是使归约过程复杂化的重要原因．本文对重写系统的歧义性进行了初步研究，并对一类常见的歧义问题作了具体分析，同时提出了解决办法．     

项重写的图实现

图重写能够有效地实现项重写。文章从项重写的图实现的角度出发，研究了图重写模拟项重写的正确性和完备性：在无环出现的情况下，图重写对一切项重写下正确；在无环出现的条件下，图重写对左线性合流的项重写是完备的。     

Conditional Term Graph Rewriting with Indirect Sharing

For reasons of efficiency, term rewriting is usually implemented by term graph rewriting. In term rewriting, expressions are represented as terms, whereas in term graph rewriting these are represented as directed graphs. Unlike terms, graphs allow a sharing of common subexpressions. In previous work, we have shown that conditional term graph rewriting is a sound and complete implementation for a certain class of CTRSs with strict equality, provided that a minimal structure sharing scheme is used. In this paper, we will show that this is also true for two different extensions of normal CTRSs. In contrast to the previous work, however, a non-minimal structure sharing scheme can be used. That is, the amount of sharing is increased.     

Mechanizing Weakly Ground Termination Proving of Term Rewriting Systems by Structural and Cover-Set Inductions

The paper presents three formal proving methods for generalized weakly ground terminating property, i.e., weakly terminating property in a restricted domain of a term rewriting system, one with structural induction, one with cover-set induction, and the third without induction, and describes their mechanization based on a meta-computation model for term rewriting systems-dynamic term rewriting calculus. The methods can be applied to non-terminating, non-confluent and/or non-left-linear term rewriting systems. They can do "forward proving" by applying propositions in the proof, as well as "backward proving" by discovering lemmas during the proof.     

Paramodulation and Knuth–Bendix Completion with Nontotal and Nonmonotonic Orderings

Up to now, all existing completeness results for ordered paramodulation and Knuth–Bendix completion have required term ordering to be well founded, monotonic, and total(izable) on ground terms. For several applications, these requirements are too strong, and hence weakening them has been a well-known research challenge.Here we introduce a new completeness proof technique for ordered paramodulation where the only properties required on are well-foundedness and the subterm property. The technique is a relatively simple and elegant application of some fundamental results on the termination and confluence of ground term rewrite systems (TRS).By a careful further analysis of our technique, we obtain the first Knuth–Bendix completion procedure that finds a convergent TRS for a given set of equations E and a (possibly non-totalizable) reduction ordering whenever it exists. Note that being a reduction ordering is the minimal possible requirement on , since a TRS terminates if, and only if, it is contained in a reduction ordering.     

Infinitary Combinatory Reduction Systems

We define infinitary Combinatory Reduction Systems (iCRSs), thus providing the first notion of infinitary higher-order rewriting. The systems defined are sufficiently general that ordinary infinitary term rewriting and infinitary λ-calculus are special cases.Furthermore, we generalise a number of known results from first-order infinitary rewriting and infinitary λ-calculus to iCRSs. In particular, for fully-extended, left-linear iCRSs we prove the well-known compression property, and for orthogonal iCRSs we prove that (1) if a set of redexes U has a complete development, then all complete developments of U end in the same term and that (2) any tiling diagram involving strongly convergent reductions S and T can be completed iff at least one of S/T and T/S is strongly convergent.We also prove an ancillary result of independent interest: a set of redexes in an orthogonal iCRS has a complete development iff the set has the so-called finite jumps property.     

Practical ultra‐reliability for abstract data types

The Term Redundancy Method (TRM) is a novel approach for obtaining ultra‐reliable programs through specification‐based testing. Current specification‐based testing schemes need a prohibitively large number of test cases for estimating ultra‐reliability. They assume the availability of an accurate program‐usage distribution prior to testing, and they assume the availability of a test oracle. This paper shows how to obtain ultra‐reliable abstract data types specified with equational specifications, with a practical number of test cases, without an accurate usage distribution, and without the usual test oracle. The effectiveness of the TRM in failure detection and recovery is demonstrated on the aircraft collision avoidance system TCAS. Copyright © 2007 John Wiley & Sons, Ltd.     

Formalizing and Analyzing the Needham-Schroeder Symmetric-Key Protocol by Rewriting

This paper reports on work in progress on using rewriting techniques for the specification and the verification of communication protocols. As in Genet and Klay's approach to formalizing protocols, a rewrite system describes the steps of the protocol and an intruder's ability of decomposing and decrypting messages, and a tree automaton encodes the initial set of communication requests and an intruder's initial knowledge. In a previous work we have defined a rewriting strategy that, given a term t that represents a property of the protocol to be proved, suitably expands and reduces t using the rules in and the transitions in to derive whether or not t is recognized by an intruder. In this paper we present a formalization of the Needham-Schroeder symmetric-key protocol and use the rewriting strategy for deriving two well-known authentication attacks.     

Regular Sets of Descendants by Leftmost Strategy

For a constructor-based rewrite system R, a regular set of ground terms E, and assuming some additional restrictions, we build a finite tree automaton that recognizes the descendants of E, i.e. the terms issued from E by rewriting, according to leftmost strategy.     

General Algorithms for Permutations in Equational Inference

Mechanized systems for equational inference often produce many terms that are permutations of one another. We propose to gain efficiency by dealing with such sets of terms in a uniform manner, by the use of efficient general algorithms on permutation groups. We show how permutation groups arise naturally in equational inference problems, and study some of their properties. We also study some general algorithms for processing permutations and permutation groups, and consider their application to equational reasoning and term-rewriting systems. Finally, we show how these techniques can be incorproated into resolution theorem-proving strategies.     

Mechanizing and Improving Dependency Pairs

The dependency pair technique is a powerful method for automated termination and innermost termination proofs of term rewrite systems (TRSs). For any TRS, it generates inequality constraints that have to be satisfied by well-founded orders. We improve the dependency pair technique by considerably reducing the number of constraints produced for (innermost) termination proofs. Moreover, we extend transformation techniques to manipulate dependency pairs that simplify (innermost) termination proofs significantly. To fully mechanize the approach, we show how transformations and the search for suitable orders can be mechanized efficiently. We implemented our results in the automated termination prover AProVE and evaluated them on large collections of examples. Supported by the Deutsche Forschungsgemeinschaft DFG, grant GI 274/5-1.