Adhesive High-Level Replacement Systems with Negative Application Conditions

The goal of this paper is the generalization of basic results for adhesive High-Level Replacement (HLR) systems to adhesive HLR systems with negative application conditions. These conditions restrict the application of a rule by expressing that a specific structure should not be present before or after applying the rule to a certain context. Such a condition influences thus each rule application or transformation and therefore changes significantly the properties of the replacement system. The effect of negative application conditions on the replacement system is described in the generalization of the following results, formulated already for adhesive HLR systems without negative application conditions: Local Church-Rosser Theorem, Parallelism Theorem, Completeness Theorem for Critical Pairs, Concurrency Theorem, Embedding and Extension Theorem and Local Confluence Theorem or Critical Pair Lemma. These important generalized results will support the development of formal analysis techniques for adhesive HLR replacement systems with negative application conditions

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

M-adhesive transformation systems with nested application conditions. Part 1: parallelism, concurrency and amalgamation

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.Nested application conditions generalise the well-known negative application conditions and are important for several application domains. In this paper, we present Local Church–Rosser, Parallelism, Concurrency and Amalgamation Theorems for rules with nested application conditions in the framework of M-adhesive categories, where M-adhesive categories are slightly more general than weak adhesive high-level replacement categories. Most of the proofs are based on the corresponding statements for rules without application conditions and two shift lemmas stating that nested application conditions can be shifted over morphisms and rules

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

Negative Application Conditions for Reconfigurable Place/Transition Systems

This paper introduces negative application conditions for reconfigurable place/transition nets. These are Petri nets together with a set of rules that allow changing the net and its marking dynamically. Negative application conditions are a control structure that prohibits the application of a rule if certain structures are already existent. We motivate the use of negative application conditions in a short example. Subsequently the underlying theory is sketched and the results – concerning parallelism, concurrency and confluence – are presented. Then we resume the example and explicitly discuss the main results and their usefulness within the example

Negative Application Conditions for Reconfigurable Algebraic High-Level Systems

This paper introduces negative application conditions for reconfigurable algebraic high-level systems. These are algebraic high-level systems, i.e. algebraic high-level nets with an initial marking, together with a set of rules for changing the system dynamically. Negative application conditions are a control structure for restricting the application of a rule if a certain structure is present. The use of negative application conditions is motivated in a short example. Subsequently, the underlying theory is sketched and the most significant results are presented. Finally, the example is resumed and the main results and their usefulness within the example are discussed

Canonical Derivations with Negative Application Conditions

Using graph transformations to specify the dynamics of distributed systems and networks, we require a precise understanding of concurrency. Negative application conditions (NACs) are an essential means for controlling the application of rules, extending our ability to model complex systems. A classical notion of concurrency in graph transformation is based on shift equivalence and its representation by canonical derivations, i.e., normal forms of the shift operation anticipating independent steps. These concepts are lifted to graph transformation systems with NACs and it is shown that canonical derivations exist for so-called incremental NACs

Reconfigurable Open Algebraic High-Level Systems

In this paper reconfigurable open algebraic high-level (AHL) systems are introduced as an extension of AHL systems [PER95]. In addition to the integration of data structures open places and communicating transitions allow modelling reactive behavior as communication with their environment. Reconfigurable open AHL systems are defined that comprise rules and transformations of these nets. Formally they are an instance of weak adhesive HLR systems [EP06] and so yield the same results. Moreover, a case study is presented that demonstrates the practical need for reconfigurable open AHL systems