Two Algebraic Process Semantics for Contextual Nets

We show that the so-called 'Petri nets are monoids' approach initiated by Meseguer and Montanari can be extended from ordinary place/transition Petri nets to contextual nets by considering suitable non-free monoids of places. The algebraic characterizations of net concurrent computations we provide cover both the collective and the individual token philosophy, uniformly along the two interpretations, and coincide with the classical proposals for place/transition Petri nets in the absence of read-arcs

Designing the automatic transformation of visual languages

AbstractThe design process of complex systems requires a precise checking of the functional and dependability attributes of the target design. The growing complexity of systems necessitates the use of formal methods, as the exhaustiveness of checks performed by the traditional simulation and testing is insufficient.For this reason, the mathematical models of various formal verification tools are automatically derived from UML-diagrams of the model by mathematical transformations guaranteeing a complete consistency between the target design and the models of verification and validation tools.In the current paper, a general framework for an automated model transformation system is presented. The method starts from a uniform visual description and a formal proof concept of the particular transformations by integrating the powerful computational paradigm of graph transformation, planner algorithms of artificial intelligence, and various concepts of computer engineering

Petri net modules in the transformation-based component framework

AbstractComponent-based software engineering needs to be backed by thorough formal concepts and modeling techniques. This paper combines two concepts introduced independently by the two authors in previous papers. On one hand, the concept of Petri net modules introduced at IDPT 2002 in Padberg [J. Padberg, Petri net modules, Journal on Integrated Design and Process Technology 6 (4) (2002) 105–120], and on the other hand a generic component framework for system modeling introduced at FASE 2002 in Ehrig et al. [H. Ehrig, F. Orejas, B. Braatz, M. Klein, M. Piirainen, A generic component concept for system modeling, in: Proceedings of FASE ’02, Lecture Notes in Computer Science, vol. 2306, Springer, 2002]. First we develop a categorical formalization of the transformation based approach to components that is based on pushouts. This is the frame in which we show that Petri net modules can be considered as an instantiation of the generic component framework. This allows applying the transformation based semantics and compositionality result of the generic framework to Petri net modules. In addition to general Petri net modules we introduce Petri net modules preserving safety properties which can be considered as another instantiation of pushout based formalization of the generic framework

Process Semantics of Petri Nets over Partial Algebra

"Petri nets are monoids" is the title and the central idea of the paper [7]. It provides an algebraic approach to define both nets and their processes as terms. A crucial assumption for this concept is that arbitrary concurrent composition of processes is defined, which holds true for place/transition Petri nets where places can hold arbitrarily many tokens. This paper defines a similar concept for elementary Petri nets, which are elementary net systems with arbitrary initial marking. Since markings of elementary nets cannot be added arbitrarily, some operators are only defined partially; hence we employ concepts of partial algebra. The main result of the paper states that the semantics based on process terms agrees with the classical partial-order process semantics for elementary net systems. More precisely, we provide a syntactic equivalence notion for process terms and a bijection from according equivalence classes of process terms to isomorphism classes of partially ordered proce..