Elisabeth Pelz

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

Closure properties of deterministic 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.

A logical approach of Petri net languages

Deterministic Petri nets, as introduced in Vidal-Naquets thesis [V] are studied here. We investigate systematically their closure properties under the standard language theoretical operations and prove in particular that the complement of a lan-guage of a deterministic net is always the language of a Petri net — which improves on both sides Hacks result on the complementation closure of free Petri net languages [H] —.

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

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.

Communication as Unification in the Petri Box Calculus

Abstract For languages recognized by finite automata we dispose of two formalisms: regular expressions (Kleene, 1956) and logical formulas (Buchi, 1960). In the case of Petri net languages there is no formalism like regular expressions. In this paper we give a Buchi-like theorem which characterizes Petri net languages in terms of second-order logical formulas. This characterization has two advantages: (1) It situates exactly the power of Petri nets with respect to finite automata; roughly speaking, Petri nets are finite automata plus the ability of testing if a string of parenthesis is well formed (in this paper ‘parenthesis’ always means the usual one sort of parentheses). (2) Given a language, it enables us to easily prove that it is a Petri net language. In addition we prove that Petri net languages and deadlock languages coincide.

A semantics of Security Protocol Language (SPL) using a class of composable high-level Petri nets

In this paper, we introduce a framework composed of a syntax and its compositional Petri net semantics, for the specification and verification of properties (like authentication) of security protocols. The protocol agents (e.g., an initiator, a responder, a server, a trusted third party, ...) are formalized as roles, each of them having a predefined behavior depending on their global and also local knowledge (including for instance public, private and shared keys), and may interact in a potentially hostile environment. The main characteristics of our framework, is that it makes explicit, structured and formal, the usually implicit information necessary to analyse the protocol, for instance the public and private contextof execution. The roles and the environment are expressed using SPL processes and compositionally translated into high-level Petri nets, while the context specifying the global and local knowledge of the participants in the protocol is used to generate the corresponding initial marking (with respect to the studied property). Finally, this representation is used to analyse the protocol properties, applying techniques of simulation and model-checking on Petri nets. The complete approach is illustrated on the case study of the Kao-Chow authentication protocol.

Small Universal Non-deterministic Petri Nets with Inhibitor Arcs

A way of handling abstract data types in the Petri Box Calculus [BDH92] is proposed. Semantic objects are A-nets, a kind of algebraic nets with Boxe like interfaces. The synchronization operation on A-nets is discussed and some basic (non-trivial) algebraic properties of the synchronization with syntactic unification are shown.

An approach to state space reduction for systems with dynamic process creation

This paper aims at introducing a Petri net semantics of security protocols allowing to study their properties formally. This is obtained by means of an economic but expressive class of composable high-level Petri nets, called S-nets, inspired from works about the relationship between Petri nets and process algebras. S-nets are applied then to give a compositional high-level Petri net semantics to SPL The Needham-Schroder protocol is employed to illustrate how this semantics can be used in order to establish the violation of the authentication property.