Algebraic High-Level Nets as Weak Adhesive HLR Categories

Adhesive high-level replacement (HLR) systems have been recently introduced as a new categorical framework for double pushout transformations. Algebraic high-level nets combine algebraic specifications with Petri nets to allow the modelling of data, data flow and data changes within the net. In this paper, we show that algebraic high-level schemas and nets fit well into the context of weak adhesive HLR categories. This allows us to apply the developed theory also to algebraic high-level net transformations

Finitary M-Adhesive Categories : Unabridged Version

Finitary M-adhesive categories are M-adhesive categories with finite objects only, where the notion M-adhesive category is short for weak adhesive high-level replacement (HLR) category. We call an object finite if it has a finite number of M-subobjects. In this paper, we show that in finitary M-adhesive categories we do not only have all the well-known properties of M-adhesive categories, but also all the additional HLR-requirements which are needed to prove the classical results for M-adhesive systems. These results are the Local Church-Rosser, Parallelism, Concurrency, Embedding, Extension, and Local Confluence Theorems, where the latter is based on critical pairs. More precisely, we are able to show that finitary M-adhesive categories have a unique E-M factorization and initial pushouts, and the existence of an M-initial object implies in addition finite coproducts and a unique E'-M' pair factorization. Moreover, we can show that the finitary restriction of each M-adhesive category is a finitary M-adhesive category and finitariness is preserved under functor and comma category constructions based on M-adhesive categories. This means that all the classical results are also valid for corresponding finitary M-adhesive systems like several kinds of finitary graph and Petri net transformation systems. Finally, we discuss how some of the results can be extended to non-M-adhesive categories

Finitary M-adhesive categories

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.Finitary M-adhesive categories are M-adhesive categories with finite objects only, where M-adhesive categories are a slight generalisation of weak adhesive high-level replacement (HLR) categories. We say an object is finite if it has a finite number of M-subobjects. In this paper, we show that in finitary M-adhesive categories we not only have all the well-known HLR properties of weak adhesive HLR categories, which are already valid for M-adhesive categories, but also all the additional HLR requirements needed to prove classical results including the Local Church-Rosser, Parallelism, Concurrency, Embedding, Extension and Local Confluence Theorems, where the last of these is based on critical pairs. More precisely, we are able to show that finitary M-adhesive categories have a unique ε'-M factorisation and initial pushouts, and the existence of an M-initial object implies we also have finite coproducts and a unique ε' -M pair factorisation. Moreover, we can show that the finitary restriction of each M-adhesive category is a finitary M-adhesive category, and finitarity is preserved under functor and comma category constructions based on M-adhesive categories. This means that all the classical results are also valid for corresponding finitary M-adhesive transformation systems including several kinds of finitary graph and Petri net transformation systems. Finally, we discuss how some of the results can be extended to non-M-adhesive categories

Reconfigurable Petri Systems with Negative Application Conditions

Diese Arbeit führt negative Anwendungsbedingungen (NACs) für verschiedene Typen von rekonfigurierbaren Petri Systemen ein. Dies sind Petri Systeme mit einer Menge von Transformationsregeln, die eine dynamische Veränderung des Petri Systems ermöglichen. Negative Anwendungsbedingungen sind eine Kontrollstruktur um die Anwendung einer Regel zu verbieten, wenn eine bestimmte Struktur vorhanden ist. Wie in [Lam07] und [LEOP08] vorgestellt, sind schwach adhäsive HLR Kategorien mit negativen Anwendungsbedingungen schwach adhäsive HLR Kategorien mit drei zusätzlichen, ausgezeichneten Morphismenklassen und einigen zusätzlichen Eigenschaften. Diese Eigenschaften werden benötigt, um Ergebnisse wie das Lokale Church-Rosser Theorem, das Parallelismustheorem, das Vollständigkeitstheorem der kritischen Paare, das Nebenläufigkeitstheorem, das Einbettungs- und das Erweiterungstheorem und das Lokale Konfluenz Theorem für die Benutzung mit negativen Anwendungsbedingungen zu verallgemeinern. Das Hauptziel dieser Arbeit besteht darin nachzuweisen, dass die Kategorien PTSys der P/T Systeme, AHLNet der AHL Netze, AHLSystems der AHL Systeme und PTSys(L) der L-gelabelten P/T Systeme schwach adhäsive HLR Kategorien mit negativen Anwendungsbedingungen sind. Dafür werden diese Kategorien formal eingeführt und die dafür benötigten Eigenschaften detailliert bewiesen. Zusätzlich wird die praktische Anwendung der erzielten Ergebnisse in Form von Fallstudien dargelegt.This thesis introduces negative application conditions (NACs) for varied kinds of reconfigurable Petri systems. These are Petri systems together with a set of transformation rules that allow changing the Petri system dynamically. Negative applications are a control structure for restricting the application of a rule if a certain structute is present. As introduced in [Lam07] and [LEOP08], (weak) adhesive high-level replacement (HLR) categories with negative application conditions are (weak) adhesive HLR categories with three additional distinguished morphism classes and some additional properties. These properties are required for generalizing results like Local Church- Rosser Theorem, Parallelism Theorem, Completeness Theorem of Critical Pairs, Concurrency Theorem, Embedding and Extension Theorem and Local Confluence Theorem for the use of negative application conditions. The main goals of this thesis are proving that the categories PTSys of P/T systems, AHLNet of algebraic high-level (AHL) nets, AHLSystems of AHL systems and PTSys(L) of L-labeled P/T systems are weak adhesive HLR categories with negative application conditions. Therefore, these categories are formally introduced and the required properties are proven in detail. Additionally, the practical application of the achieved results is presented in form of case studies

Generalised compositionality in graph transformation

We present a notion of composition applying both to graphs and to rules, based on graph and rule interfaces along which they are glued. The current paper generalises a previous result in two different ways. Firstly, rules do not have to form pullbacks with their interfaces; this enables graph passing between components, meaning that components may “learn” and “forget” subgraphs through communication with other components. Secondly, composition is no longer binary; instead, it can be repeated for an arbitrary number of components

Reconfigurable Decorated PT Nets with Inhibitor Arcs and Transition Priorities

In this paper we deal with additional control structures for decorated PT Nets. The main contribution are inhibitor arcs and priorities. The first ensure that a marking can inhibit the firing of a transition. Inhibitor arcs force that the transition may only fire when the place is empty. an order of transitions restrict the firing, so that an transition may fire only if it has the highest priority of all enabled transitions. This concept is shown to be compatible with reconfigurable Petri nets

Satisfaction, Restriction and Amalgamation of Constraints in the Framework of M-Adhesive Categories

Application conditions for rules and constraints for graphs are well-known in the theory of graph transformation and have been extended already to M-adhesive transformation systems. According to the literature we distinguish between two kinds of satisfaction for constraints, called general and initial satisfaction of constraints, where initial satisfaction is defined for constraints over an initial object of the base category. Unfortunately, the standard definition of general satisfaction is not compatible with negation in contrast to initial satisfaction. Based on the well-known restriction of objects along type morphisms, we study in this paper restriction and amalgamation of application conditions and constraints together with their solutions. In our main result, we show compatibility of initial satisfaction for positive constraints with restriction and amalgamation, while general satisfaction fails in general. Our main result is based on the compatibility of composition via pushouts with restriction, which is ensured by the horizontal van Kampen property in addition to the vertical one that is generally satisfied in M-adhesive categories.Comment: In Proceedings ACCAT 2012, arXiv:1208.430

Mechanical performance of composite bonded joints in the presence of localised process-induced zero-thickness defects

Processing parameters and environmental conditions can introduce variation into the performance of adhesively bonded joints. The effect of such variation on the mechanical performance of the joints is not well understood. Moreover, there is no validated nondestructive inspection (NDI) available to ensure bond integrity post-process and in-service so as to guarantee initial and continued airworthiness in aerospace sector. This research studies polymer bond defects produced in the laboratory scale single-lap composite-to-composite joints that may represent the process-induced defects occurring in actual processing scenarios such as composite joining and repair in composite aircrafts. The effect of such defects on the degradation of a joint's mechanical performance is then investigated via quasi-static testing in conjunction with NDI ultrasonic C-scanning and pulsed thermography. This research is divided into three main sections: 1- manufacturing carbon fibre-reinforced composite joints containing representative nearly zero-thickness bond defects, 2- mechanical testing of the composite joints, and 3- assessment of the NDI capability for detection of the bond defects in such joints