Counterexamples in infinitary rewriting with non-fully-extended rules

We show counterexamples exist to confluence modulo hypercollapsing subterms, fair normalisation, and the normal form property in orthogonal infinitary higher-order rewriting with non-fully-extended rules. This sets these systems apart from both fully-extended and finite systems, where no such counterexamples are possible.     

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.     

From Chemical Rules to Term Rewriting

In this paper, rule-based programming is explored in the field of automated generation of chemical reaction mechanisms. We explore a class of graphs and a graph rewriting relation where vertices are preserved and only edges are changed. We show how to represent cyclic labeled graphs by decorated labeled trees or forests, then how to transform trees into terms. A graph rewriting relation is defined, then simulated by a tree rewriting relation, which can be in turn simulated by a rewriting relation on equivalence classes of terms. As a consequence, this kind of graph rewriting can be implemented using term rewriting. This study is motivated by the design of the GasEl system for the generation of kinetics reactions mechanisms. In GasEl, chemical reactions correspond to graph rewrite rules and are implemented by conditional rewriting rules in ELAN. The control of their application is done through the ELAN strategy language.     

A Characterization of Weakly Church–Rosser Abstract Reduction Systems That Are Not Church–Rosser

Basic properties of rewriting systems can be stated in the framework of abstract reduction systems (ARS). Properties like confluence (or Church–Rosser, CR) and weak confluence (or weak Church–Rosser, WCR) and their relationships can be studied in this setting: as a matter of fact, well-known counterexamples to the implication WCR CR have been formulated as ARS. In this paper, starting from the observation that such counterexamples are structurally similar, we set out a graph-theoretic characterization of WCR ARS that is not CR in terms of a suitable class of reduction graphs, such that in every WCR not CR ARS, we can embed at least one element of this class. Moreover, we give a tighter characterization for a restricted class of ARS enjoying a suitable regularity condition. Finally, as a consequence of our approach, we prove some interesting results about ARS using the mathematical tools developed. In particular, we prove an extension of the Newman's lemma and we find out conditions that, once assumed together with WCR property, ensure the unique normal form property. The Appendix treats two interesting examples, both generated by graph-rewriting rules, with specific combinatorial properties.     

A Framework for Operational Equational Specifications with Pre-defined Structures

We present a general framework for studying equational specifications with pre-defined structures. The axioms of the specifications are to define new structures in addition to the given ones. In particular, they may define a new operator only partially over some given domain. Our approach allows one to assign easily semantics to such specifications in a denotational and operational fashion. In order to enable functional-style computations, we introduce a semantically enriched notion of term rewriting. This rewrite relation also allows us to infer the consistency of the specification. For the latter purpose one has to show confluence modulo the given structures. We outline how to obtain criteria easily for confluence and termination of the rewrite relation of discourse by generalizing results of the classical syntactic rewrite theory.     

External Rewriting for Skeptical Proof Assistants

This paper presents the design, the implementation, and experiments of the integration of syntactic, conditional possibly associative-commutative term rewriting into proof assistants based on constructive type theory. Our approach is called external because it consists in performing term rewriting in a specific and efficient environment and checking the computations later in a proof assistant. Two typical systems are considered in this work: ELAN, based on the rewriting calculus, as the term rewriting-based environment, and Coq, based on the calculus of inductive constructions as the proof assistant. We first formalize the proof terms for deduction by rewriting and strategies in ELAN using the rewriting calculus with explicit substitutions. We then show how these proof terms can soundly be translated into Coq syntax where they can be directly type checked. For the method to be applicable for rewriting modulo associativity and commutativity, we provide an effective method to prove equalities modulo these axioms in Coq using ELAN. These results have been integrated into an ELAN-based rewriting tactic in Coq.     

Inequational Deduction as Term Graph Rewriting

Multi-algebras allow to model nondeterminism in an algebraic framework by interpreting operators as functions from individual arguments to sets of possible results.We propose a simple inequational deduction system, based on term graphs, for inferring inclusions of derived relations in a multi-algebra, and we show that term graph rewriting provides a sound and complete implementation of it.     

Structure and Properties of Traces for Functional Programs

The tracer Hat records in a detailed trace the computation of a program written in the lazy functional language Haskell. The trace can then be viewed in various ways to support program comprehension and debugging. The trace was named the augmented redex trail. Its structure was inspired by standard graph rewriting implementations of functional languages. Here we describe a model of the trace that captures its essential properties and allows formal reasoning. The trace is a graph constructed by graph rewriting but goes beyond simple term graphs. Although the trace is a graph whose structure is independent of any rewriting strategy, we define the trace inductively, thus giving us a powerful method for proving its properties.     

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。     

Formal systems for gene assembly in ciliates

DNA processing in ciliates, a very ancient group of organisms, is among the most sophisticated DNA processing in living organisms. It has a quite clear computational structure and even uses explicitly the linked list data structure! Particularly interesting from the computational point of view is the process of gene assembly from its micronuclear to its macronuclear form. We investigate here the string rewriting and the graph rewriting models of this process, involving three molecular operations, which together form a universal set of operations in the sense that they can assembly any macronuclear gene from its micronuclear form. In particular we prove that although the graph rewriting system is more “abstract” than the string rewriting system, no “essential information” is lost, in the sense that one can translate assembly strategies from one system into the other.     

一种基于模重写系统的攻击者推理方法

为了解决安全协议验证中攻击者模等式理论推理的可操作性问题,提出并设计了一种基于模重写系统的攻击者推理方法。该方法建立在一个反映两种密码原语代数特性的联合理论实例之上,由一组定向的重写规则和非定向的等式构成,前者进一步转化为项重写系统TRS(Term Rewriting System),而后者则转化为有限等价类理论,通过定义项间的模重写关系,使二者构成一个可以反映攻击者针对联合理论代数项操作能力的模重写系统。实例分析表明,该模型为攻击者模等式推理规则赋予了明确的操作语义,可以使攻击者达到对安全协议代数项规约、推理的目的。     

A Categorical Critical-pair Completion Algorithm

We introduce a general critical-pair/completion algorithm, formulated in the language of category theory. It encompasses the Knuth–Bendix procedure for term rewriting systems (also modulo equivalence relations), the Gröbner basis algorithm for polynomial ideal theory, and the resolution procedure for automated theorem proving. We show how these three procedures fit in the general algorithm, and how our approach relates to other categorical modeling approaches to these algorithms, especially term rewriting.     

Rewrite rule systems for modal propositional logic

This paper explains new results relating modal propositional logic and rewrite rule systems. More precisely, we give complete term rewriting systems for the modal propositional systems known as K, Q, T, and S5. These systems are presented as extensions of Hsiang's system for classical propositional calculus. We have checked local confluence with the rewrite rule system K.B. (cf. the Knuth-Bendix algorithm) developed by the Formel project at INRIA. We prove that these systems are noetherian, and then infer their confluence from Newman's lemma. Therefore each term rewriting system provides a new automated decision procedure and defines a canonical form for the corresponding logic. We also show how to characterize the canonical forms thus obtained.     

Reaction Graph

The paper proposes reaction graphs as graphical representations of computational objects.A reaction graph is a directed graph with all its arrows and some of its nodes labeled.Computations are modled by graph rewriting of a simple nature.The basic rewriting rules embody the essence of both the communications among processes and cut-eliminations in proofs.Calculi of graphs are ideentified to give a formal and algebraic account of reaction graphs in the spirit of process algebra.With the help of the calculi,it is demonstrated that reaction graphs capture many interesting aspects of computations.     

Parallel complexity of signed graphs for gene assembly in ciliates

We consider a graph-based model for the study of parallelism in ciliate gene assembly, where a signed graph is associated to each micronuclear gene and the gene assembly is modeled as a graph rewriting process. A natural measure of complexity for gene assembly counts the minimal number of parallel steps needed to reduce the associated signed graph. We investigate the complexity of several classes of the graphs, so far found graphs of parallel complexity up to six. The general problem of whether there exists a finite upper bound for the graph parallel complexity still remains open.     

A kernel language for programmed rewriting of (hyper)graphs

The paper presents a formalism for rewriting (hyper)graphs in a controlled manner. This formalism is essentially a simple programming language with productions, that is rewriting rules, playing the role of basic instructions. Programs in this language are built from productions by means of rather standard constructors, including a parallel composition. They may contain parameters to point to specific elements of graphs to which they are supposed to be applied. Programs are intended to describe how to transform a graph and a valuation of parameters in this graph in order to reach a resulting graph and a resulting valuation of parameters.     

A kernel language for programmed rewriting of (hyper)graphs

The paper presents a formalism for rewriting (hyper)graphs in a controlled manner. This formalism is essentially a simple programming language with productions, that is rewriting rules, playing the role of basic instructions. Programs in this language are built from productions by means of rather standard constructors, including a parallel composition. They may contain parameters to point to specific elements of graphs to which they are supposed to be applied. Programs are intended to describe how to transform a graph and a valuation of parameters in this graph in order to reach a resulting graph and a resulting valuation of parameters. Received July 13, 1994 / May 2, 1995     

Modeling and Verifying Graph Transformations in Proof Assistants

This paper takes first steps towards a formalization of graph transformations in a general setting of interactive theorem provers, which will form the basis for proofs of correctness of graph transformation systems. Whereas graph rewriting is usually performed by mapping a pattern graph into a source graph by means of a graph morphism and then carrying out operations on the image node and edge set, this article generalises the notion of pattern graph to path expressions, which are formulae in a fragment of first-order logic. We examine the correspondence with traditional graph rewriting and show that this interpretation is beneficial when formally reasoning about model transformations with the aid of proof assistants.     

含假结RNA二级结构类的图语法

用最小自由能法预测RNA二级结构是NP困难问题,其根本原因是假结的存在。近几年的预测算法都针具有一定结构特征的假结寻找多项式时间算法进行预测。论文针对RNA二级结构图提出一种图语法,该语法由初始结构图集和重写规则集构成,用重写规则在初始结构图上的不断重写得到的结构图都是该语法的语言。分析了5个主流RNA二级结构预测算法的目标集,给出它们的图语法,使得目标集的结构特征一目了然,目标集间的真包含关系也通过图语法直观地体现出来。     

高分辨率彩色图形的通用拷贝方法

本文介绍一种高分辨率彩色图形的通用拷贝方法,该方法可以指定所要拷贝的图形颜色和拷贝图形的比例,在一般的24针打印机上拷贝出来。本文以EGA/VGA为例介绍了EGA/VGA图形显示的原理和图形内存数据的存取方法,24针打印机的图形打印的工作方式,取EGA/VGA的图形内存映像数据后经过滤色转换成打印机的打印格式数据的编程技巧,程序驻留内存的处理方法,图形拷贝参数的带入方法。