Unifying the syntax and semantics of modular extensions of Petri nets

Abstract

Petri nets are a modeling formalism that allows to describe concurrent systems with an intuitive and at the same time formal notation. When trying to represent real world-sized systems, the most simple versions of Petri nets tend to be extremely complex. To overcome this problem, a mandatory principle is modularity. Modular variants of Petri nets allow to create complex models by combining smaller entities. This facilitates the modeling and verification of large systems by applying a divide and conquer approach and promoting reuse. Modularity includes a wide range of notions such as encapsulation, hierarchy and instantiation. Over the years, Petri nets have been extended to include these mechanisms in many different ways. The heterogeneity of such extensions and their definitions makes it difficult to reason about their common features at a general level. This thesis proposes an approach to standardize the syntax and semantics of modular Petri nets formalisms, with the objective of gathering even the most complex modular features from the literature. The central component of this approach is a new Petri nets formalism, called the Llamas Language for Advanced Modular Algebraic Systems (LLAMAS). The main objective of LLAMAS is to be expressive enough to represent most if not all the modular Petri nets formalisms in the literature. By this, we mean that it should be possible to create a translation from every modular variant of Petri nets to LLAMAS that preserves its transition relation. This thesis introduces LLAMAS both in a light informal way and with a detailed formalization. We thoroughly describe its main features, and we give some examples of formalisms that can be translated, chosen among the most representative modular formalisms in the literature. Our approach has two positive outcomes. First, the definition of new formalisms is facilitated, by providing common ground for the definition of their semantics. Second, it is possible to reason at a general level on the most advanced verification techniques, such as the recent advances in the domain of decision diagrams.