scholarly journals Объектно-ориентированные данные как перезаписывающие системы

2015 ◽  
Author(s):  
A.E. Gutman
Keyword(s):  
Object Oriented ◽  
Conceptual Scheme ◽  
Data Systems ◽  
Rewriting Systems ◽  
Rewriting System ◽  
Rewriting Rules

A deterministic longest-prefix rewriting system is a rewriting system such that there are no rewriting rules X→Y, X→Z with Y≠Z, and only longest prefixes of words are subject to rewriting. Given such a system, analogs are defined and examined of some concepts related to object-oriented data systems: inheritance of classes and objects, instances of classes, class and instance attributes, conceptual dependence and consistency, conceptual scheme, types and subtypes, etc. A special attention is paid to the effective verification of various properties of the rewriting systems under consideration. In particular, algorithms are presented for answering the following questions: Are all words finitely rewritable? Do there exist recurrent words? Is the system conceptually consistent? Given two words X and Y, does X conceptually depend on Y? Does the type of X coincide with that of Y? Is the type of X a subtype of that of Y?

A Graph Grammar Approach to Artificial Life

2004 ◽  
Vol 10 (4) ◽  
pp. 413-431 ◽  
Author(s):  
Ole Kniemeyer ◽  
Gerhard H. Buck-Sorlin ◽  
Winfried Kurth
Keyword(s):  
Artificial Life ◽  
Regulatory Networks ◽  
Object Oriented ◽  
Graph Grammar ◽  
Lindenmayer Systems ◽  
Rewriting Systems ◽  
Flower Morphogenesis ◽  
Formal Framework ◽  
High Level ◽  
Rewriting Rules

We present the high-level language of relational growth grammars (RGGs) as a formalism designed for the specification of ALife models. RGGs can be seen as an extension of the well-known parametric Lindenmayer systems and contain rule-based, procedural, and object-oriented features. They are defined as rewriting systems operating on graphs with the edges coming from a set of user-defined relations, whereas the nodes can be associated with objects. We demonstrate their ability to represent genes, regulatory networks of metabolites, and morphologically structured organisms, as well as developmental aspects of these entities, in a common formal framework. Mutation, crossing over, selection, and the dynamics of a network of gene regulation can all be represented with simple graph rewriting rules. This is demonstrated in some detail on the classical example of Dawkins' biomorphs and the ABC model of flower morphogenesis: other applications are briefly sketched. An interactive program was implemented, enabling the execution of the formalism and the visualization of the results.

scholarly journals Diamond Subgraphs in the Reduction Graph of a One-Rule String Rewriting System

2021 ◽  
Vol 178 (3) ◽  
pp. 173-185
Author(s):  
Arthur Adinayev ◽  
Itamar Stein
Keyword(s):  
Isomorphism Problem ◽  
Complete Characterization ◽  
Hasse Diagram ◽  
Subgraph Isomorphism ◽  
Rewriting Systems ◽  
Rewriting System ◽  
String Rewriting ◽  
Reduction Graph

In this paper, we study a certain case of a subgraph isomorphism problem. We consider the Hasse diagram of the lattice Mk (the unique lattice with k + 2 elements and one anti-chain of length k) and find the maximal k for which it is isomorphic to a subgraph of the reduction graph of a given one-rule string rewriting system. We obtain a complete characterization for this problem and show that there is a dichotomy. There are one-rule string rewriting systems for which the maximal such k is 2 and there are cases where there is no maximum. No other intermediate option is possible.

Coherence of subsumption, minimum typing and type-checking in F ≤

1992 ◽  
Vol 2 (1) ◽  
pp. 55-91 ◽  
Author(s):  
Pierre-Louis Curien ◽  
Giorgio Ghelli
Keyword(s):  
Normal Form ◽  
Type System ◽  
Lambda Calculus ◽  
Complete Information ◽  
Second Order ◽  
Semantic Interpretation ◽  
Type Checking ◽  
Rewriting System ◽  
Different Types ◽  
Rewriting Rules

A subtyping relation ≤ between types is often accompanied by a typing rule, called subsumption: if a term a has type T and T≤U, then a has type U. In presence of subsumption, a well-typed term does not codify its proof of well typing. Since a semantic interpretation is most naturally defined by induction on the structure of typing proofs, a problem of coherence arises: different typing proofs of the same term must have related meanings. We propose a proof-theoretical, rewriting approach to this problem. We focus on F≤, a second-order lambda calculus with bounded quantification, which is rich enough to make the problem interesting. We define a normalizing rewriting system on proofs, which transforms different proofs of the same typing judgement into a unique normal proof, with the further property that all the normal proofs assigning different types to a given term in a given environment differ only by a final application of the subsumption rule. This rewriting system is not defined on the proofs themselves but on the terms of an auxiliary type system, in which the terms carry complete information about their typing proof. This technique gives us three different results:— Any semantic interpretation is coherent if and only if our rewriting rules are satisfied as equations.— We obtain a proof of the existence of a minimum type for each term in a given environment.— From an analysis of the shape of normal form proofs, we obtain a deterministic typechecking algorithm, which is sound and complete by construction.

REWRITING SYSTEMS IN ALTERNATING KNOT GROUPS

2006 ◽  
Vol 16 (04) ◽  
pp. 749-769 ◽  
Author(s):  
FABIENNE CHOURAQUI
Keyword(s):  
Word Problem ◽  
Rewriting Systems ◽  
Rewriting System ◽  
Regular Position

Every tame, prime and alternating knot is equivalent to a tame, prime and alternating knot in regular position, with a common projection. In this work, we show that the augmented Dehn presentation of the knot group of a tame, prime, alternating knot in regular position, with a common projection has a finite and complete rewriting system. This provides an algorithm for solving the word problem with this presentation and we find an algorithm for solving the word problem with the Dehn presentation also.

COMPLETE REWRITING SYSTEMS FOR CODIFIED SUBMONOIDS

2005 ◽  
Vol 15 (02) ◽  
pp. 207-216
Author(s):  
ANTÓNIO MALHEIRO
Keyword(s):  
The Other ◽  
Maximal Subgroups ◽  
Rewriting Systems ◽  
Group Of Units ◽  
Rewriting System ◽  
Other Hand

Given a complete rewriting system R on X and a subset X0 of X+ satisfying certain conditions, we present a complete rewriting system for the submonoid of M(X;R) generated by X0. The obtained result will be applied to the group of units of a monoid satisfying H1 = D1. On the other hand we prove that all maximal subgroups of a monoid defined by a special rewriting system are isomorphic.

scholarly journals The impact of usage of post object-oriented technologies on defect reduction in software maintenance

2019 ◽  
Keyword(s):  
Quality Improvement ◽  
Software Quality ◽  
Software Maintenance ◽  
Object Oriented ◽  
Maintenance Phase ◽  
Conceptual Scheme ◽  
Defect Reduction ◽  
Quality Improvement Research ◽  
Residual Defect ◽  
The Impact

The article is dedicated to software quality improvement research within the maintenance phase based on post-object-oriented technologies. An important problem of the maintenance phase is surveyed, namely, the crosscutting functionality problem. Mechanisms of post-object-oriented technologies have been reviewed and basic tasks to be resolved have been formulated in order to reach the final goal of the research: defect reduction during the maintenance phase. The post object-oriented technologies utilization framework for software quality improvement based on a collection of 4 heuristic assumptions has been introduced. The conceptual scheme of the framework has been presented. An applied 2-steps procedure for defect reduction assessment based on quantitative crosscutting-functionality and defect metrics has been described. Twelve results of the experiments concerning calculation of the residual defect number have been presented and analyzed.

scholarly journals Subgroups of finite index in groups with finite complete rewriting systems

2000 ◽  
Vol 43 (1) ◽  
pp. 177-183 ◽  
Author(s):  
S. J. Pride ◽  
Jing Wang
Keyword(s):  
Free Group ◽  
Finite Index ◽  
Rewriting Systems ◽  
Rewriting System

AbstractWe show that if a group G has a finite complete rewriting system, and if H is a subgroup of G with |G : H| = n, then H * Fn–1 also has a finite complete rewriting system (where Fn–1 is the free group of rank n – 1).

scholarly journals Parallel Multiset Rewriting Systems with Distorted Rules

Processes ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 347
Author(s):  
Cristina Sburlan ◽  
Dragoş-Florin Sburlan
Keyword(s):  
A Priori ◽  
Rewriting Systems ◽  
Computational Universality ◽  
Level 1 ◽  
Robust Systems ◽  
Rewriting Rules

Most of the parallel rewriting systems which model (or which are inspired by) natural/artificial phenomena consider fixed, a priori defined sets of string/multiset rewriting rules whose definitions do not change during the computation. Here we modify this paradigm by defining level-t distorted rules—rules for which during their applications one does not know the exact multiplicities of at most t∈N species of objects in their output (although one knows that such objects will appear at least once in the output upon the execution of this type of rules). Subsequently, we define parallel multiset rewriting systems with t-distorted computations and we study their computational capabilities when level-1 distorted catalytic promoted rules are used. We construct robust systems able to cope with the level-1 distortions and prove the computational universality of the model.

REWRITING SYSTEMS AND ORDERINGS ON ARTIN MONOIDS

2007 ◽  
Vol 17 (01) ◽  
pp. 61-75 ◽  
Author(s):  
PATRICK BAHLS ◽  
TYLER SMITH
Keyword(s):  
Rewriting Systems ◽  
Large Type ◽  
Rewriting System

In this paper we introduce a complete rewriting system on any large-type Artin monoid. The rewriting system stems from a well-ordering defined by Burckel on the related class of braid monoids. As a consequence of our rewriting system's existence we will recover the fact that certain large-type monoids are well-orderable, and we will discern finer detail regarding the structure of this associated ordering.

MONOIDS PRESENTED BY REWRITING SYSTEMS AND AUTOMATIC STRUCTURES FOR THEIR SUBMONOIDS

2009 ◽  
Vol 19 (06) ◽  
pp. 771-790 ◽  
Author(s):  
ALAN J. CAIN
Keyword(s):  
New Technique ◽  
Finitely Generated ◽  
Automatic Structures ◽  
Rewriting Systems ◽  
Rewriting System ◽  
Open Questions ◽  
Automatic Structure ◽  
A New Technique

This paper studies rr-, ℓr-, rℓ-, and ℓℓ-automatic structures for finitely generated submonoids of monoids presented by confluent rewriting system that are either finite and special or regular and monadic. A new technique is developed that uses an automaton to "translate" between words in the original rewriting system and words over the generators for the submonoid. This is applied to show that the submonoid inherits any notion of automatism possessed by the original monoid. Generalizations of results of Otto and Ruškuc are thus obtained: every finitely generated submonoid of a monoid presented by a confluent finite special rewriting system admits an automatic structure that is simultaneously rr-, ℓr-, rℓ-, and ℓℓ-automatic; and every finitely generated submonoid of a monoid presented by a confluent regular monadic rewriting system admits an automatic structure that is simultaneously rr- and ℓℓ-automatic. These structures are shown to be effectively computable. An algorithm is given to decide whether the monoid presented by a confluent monadic finite rewriting system is ℓr- or rℓ-automatic. Finally, these results are applied to yield answers to some hitherto open questions and to recover and generalize established results.

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