Hanna Klaudel

M-nets: An algebra of high-level Petri nets, with an application to the semantics of concurrent programming languages

Abstract. This paper describes a high-level Petri net model called M-nets (for modular multilabelled nets). A distinctive feature of this model is that it allows both: unfolding, as do most other high-level net models; and composition – in particular, synchronisation – in a process algebraic style, turning the set of M-nets into an algebraic domain. It turns out that the composition operations of this domain have various algebraic properties. Moreover, the model is such that composition operations are coherent with unfolding, in the sense that the unfolding of a composite high-level net is the composition of the unfoldings of its components. One of the motivations for M-nets is that they be a vehicle for giving semantics of concurrent programming languages. To illustrate their capability for that, the compositional semantics of

A class of composable high level Petri nets

B(PN)^2

Modeling multi-valued genetic regulatory networks using high-level petri nets

– a simple, expressive concurrent programming language – is given. An associated low-level net semantics is described, and the coherence of these high-level and low-level semantics is proved.

An M-net Semantics of B(PN)2

In this paper a high-level Petri net model called M-nets (for multilabeled nets) is developed. A distinctive feature of this model is that it allows not only vertical unfolding, as do most other high-level net models, but also horizontal composition — in particular, synchronisation — in a manner similar to process algebras such as CCS. This turns the set of M-nets into a domain whose composition operations satisfy various algebraic properties. The operations are shown to be consistent with unfolding in the sense that the unfolding of a composite high-level net is the composition of the unfoldings of its components. A companion paper shows how this algebra can be used to define the semantics of a concurrent programming language compositionally.

Asynchronous Links in the PBC and M-Nets

Regulatory networks are at the core of all biological functions from bio-chemical pathways to gene regulation and cell communication processes. Because of the complexity of the interweaving retroactions, the overall behavior is difficult to grasp and the development of formal methods is needed in order to confront the supposed properties of the biological system to the model. We revisit here the tremendous work of R. Thomas and show that its binary and also its multi-valued approach can be expressed in a unified way with high-level Petri nets. A compact modeling of genetic networks is proposed in which the tokens represent genes expression levels and their dynamical behavior depends on a certain number of biological parameters. This allows us to take advantage of techniques and tools in the field of high-level Petri nets. A developed prototype allows a biologist to verify systematically the coherence of the system under various hypotheses. These hypotheses are translated into temporal logic formulae and the model-checking techniques are used to retain only the models whose behavior is coherent with the biological knowledge.

A compositional Petri net translation of general π -calculus terms

Using a class of high level Petri nets, M-nets, endowed with composition operators resembling those of CCS, we give the compositional semantics of B(PN)2 - a syntactically simple but semantically powerful concur-rent programming language. We also give an associated low level net semantics and show the consistency of these high and low level semantics, as well as consistency with a previously defined low level semantics of B(PN)2.

General parameterised refinement and recursion for the M-net calculus

This paper aims at introducing an extension of M-nets, a fully compositional class of high-level Petri nets, and of its low-level counter part, Petri Boxes Calculus (PBC). We introduce a new operator with nice algebraic properties which allows to express asynchronous communications in a simple and flexible way. With this extension, asynchronous communications become at least as simple to express as (existing) synchronous ones. Finally, we show how this extension can be used in order to specify systems with timing constraints.

Petri nets with causal time for system verification

We propose a finite structural translation of possibly recursive π-calculus terms into Petri nets. This is achieved by using high-level nets together with an equivalence on markings in order to model entering into recursive calls, which do not need to be guarded. We view a computing system as consisting of a main program (π-calculus term) together with procedure declarations (recursive definitions of π-calculus identifiers). The control structure of these components is represented using disjoint high-level Petri nets, one for the main program and one for each of the procedure declarations. The program is executed once, while each procedure can be invoked several times (even concurrently), each such invocation being uniquely identified by structured tokens which correspond to the sequence of recursive calls along the execution path leading to that invocation.

General Refinement for High Level Petri Nets

The algebra of M-nets, a high-level class of labelled Petri nets, was introduced in order to cope with the size problem of the low-level Petri box calculus, especially when applied as semantical domain for parallel programming languages. General, unrestricted and parameterised refinement and recursion operators, allowing to represent the (possibly recursive and concurrent) procedure call mechanism, are introduced into the M-net calculus.

Modeling and Analysis of Security Protocols Using Role Based Specifications and Petri Nets

We present a new approach to the modelling of time constrained systems. It is based on untimed high-level Petri nets using the concept of causal time. With this concept, the progression of time is modelled in the system by the occurrence of a distinguished event, tick, which serves as a reference to the rest of the system. In order to validate this approach as suitable for automated verification, a case study is provided and the results obtained using a model-checker on high-level Petri nets are compared with those obtained for timed automata using prominent tools. The comparison is encouraging and shows that the causal time approach is intuitive and modular. It also potentially allows for efficient verification.