Reconfigurable Petri Systems with Negative Application Conditions

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 ChurchRosser 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.