Regular Event Structures and Finite Petri Nets: A Conjecture

In this paper, we deal with the problem of critical observability for discrete event systems modeled by labeled safe Petri nets (PNs). Critical observability is a property originated from the safety-critical applications of cyber-physical systems. For the purpose to check this property of a PN model, it is necessary to detect whether the current state of the net system is, or is not in a set of critical states representing dangerous operations. The main results of the work is to propose a necessary and sufficient condition for checking the critical observability in safe PNs when the set of critical states is modeled by an arbitrary set of reachable markings. The proposed method exploits the solution of integer linear programming problems. Finally, several examples are discussed to demonstrate the efficiency of the proposed approach.

Event Structures for Local Traces

In this paper we propose a technique for verification of mobile systems. We translate finite control processes, which are a well-known subset of π-Calculus, into Petri nets, which are subsequently used for model checking. This translation always yields bounded Petri nets with a small bound, and we develop a technique for computing a non-trivial bound by static analysis. Moreover, we introduce the notion of safe processes, which are a subset of finite control processes, for which our translation yields safe Petri nets, and show that every finite control process can be translated into a safe one of at most quadratic size. This gives a possibility to translate every finite control process into a safe Petri net, for which efficient unfolding-based verification is possible. Our experiments show that this approach has a significant advantage over other existing tools for verification of mobile systems in terms of memory consumption and runtime.Keywordsfinite control processessafe processesπ-Calculusmobile systemsmodel checkingPetri net unfoldings

International audience

When a Petri net is synthesised from a labelled transition system, it is frequently desirable that certain additional constraints are fulfilled. For example, in circuit design, one is often interested in constructing safe Petri nets. Targeting such subclasses of Petri nets is not necessarily computationally more efficient than targeting the whole class. For example, targeting safe nets is known to be NP-complete while targeting the full class of place/transition nets is polynomial, in the size of the transition system. In this paper, several classes of Petri nets are examined, and their suitability for being targeted through efficient synthesis from labelled transition systems is studied and assessed. The focus is on choice-free Petri nets and some of their subclasses. It is described how they can be synthesised efficiently from persistent transition systems, summarising and streamlining in tutorial style some of the authors’ and their groups’ work over the past few years.

It is shown how to study the latency of packets exchanged by MIMD distributed memory architectures with regular structures. To reach this goal, the single node, the architecture topology, the routing algorithm, and the flow control algorithm are modeled. Models have been built with the formalism of stochastic well-formed coloured Petri nets (SWNs) having in mind modularity. Different types of nodes, topology, routing, and flow control are modeled in isolation and are then intermixed to study different architectures. To achieved simplicity and modularity, SWNs are used to their full power, so that this work constitutes quite a complete example of modeling with SWNs. >

We review the conceptual development of (true) concurrency and branching time starting from Petri nets and proceeding via Mazurkiewicz traces, pomsets, bisimulation, and event structures up to higher dimensional automata (HDAs), whose acyclic case may be identified with triadic event structures and triadic Chu spaces. Acyclic HDAs may be understood as extending the two truth values of Boolean logic with a third value .

<p>This paper introduces a non-interleaved model for the behaviour of distributed computing systems, and an accompanying temporal logic with an explicit treatment of concurrency (based on a notion of local rather than global states).</p><p>A subclass of event structures (called n-agent event structures) is used as the underlying model -- intended to describe the computational behaviour of n communicating, sequential (and possibly non-deterministic) agents. The logic is centered around indexed modalities to describe the states of knowledge of the individual agents during such a computation.</p><p>An axiom system for the logic is presented, and a full proof of its soundness and completeness (Henkin style proof) is given.</p>

The problem of extending to graph grammars the unfolding semantics originally developed by Winskel for (safe) Petri nets has been faced several times along the years, both for the single-pushout and double-pushout approaches, but only partial results were obtained. In this paper we fully extend Winskel’s approach to single-pushout grammars providing them with a categorical concurrent semantics expressed as a coreflection between the category of graph grammars and the category of prime algebraic domains.

A method to find the minimized state machine cover of live and safe Petri nets (PNs) is proposed in this paper. It is required that a cover be obtained in some implementation methods of PN-based control algorithms and other applications such as data mining. Most of the known methods of its computation have at least exponential time and space complexity; this is true not only for the methods which guarantee a minimal cover is obtained but also for some methods of finding approximate solutions. The proposed algorithm is an approximation algorithm and has polynomial computational complexity. The experimental verification shows a very high efficiency of the presented technique. The proposed method is especially valuable in the case of large systems where a solution is obtained hundreds of times quicker than by other methods.

We introduce infinitary partial languages for Petri nets and study some of their properties. Earlier results on the interrelation between various Petri net semantics for finite behaviour are shown to be valid for infinite behaviour. As a consequence step sequences and event structures of processes both can be taken as a semantics for Petri nets without any loss of information.Via the introduction of infinite partial words it is possible to express the properties of justice and fairness in a natural way: justice can be characterized as maximality of progress and fairness as ‘fair’ conflict resolution. By this we overcome the ambiguity arising from the lack of discrimination between concurrency and non-determinism in the sequential approach.

Petri nets generating all the 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> binary n-vectors as their marking vectors are not only of theoretical interest but also are of practical importance. In this note, we demonstrate the existence of a disconnected 1-safe Petri net whose reachability tree is homomorphic to the n-dimensional complete lattice L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> . This makes the problem of characterizing the 1-safe Petri nets that generate all the binary n-vectors as marking vectors exactly once appear more intricate.

Non-interference characterises the absence of undesired information flows in a computing system, by asking that actions with higher level of confidentiality do not cause any observable effect at the lower levels. In many concrete applications, this requirement is too strict and the abstract model is enriched with some form of downgrading, namely with the possibility of declassifying information, thus allowing for a controlled form of leakage. This paper focuses on BINI (Bisimilarity-based Intransitive non-interference), a formalisation of non-interference with downgrading in the setting of Petri nets. Generalising some previous works, we provide a causal characterisation of BINI in terms of the unfolding semantics, a true concurrent semantics of Petri nets. Building on this, we design an algorithm for checking BINI on safe Petri nets which relies on the construction of suitable complete prefixes of the unfolding. The algorithm is implemented in a prototype tool and some preliminary tests are quite encouraging as they suggest that the management of downgrading does not cause any significant performance decay.

A definition of “action refinement” is given for an operational model of concurrent processes based on safe Petri Nets, generalizing previous work of Vogler and van Glabbeek/Goltz. A failure-style denotational semantics is described for process nets. The semantics is fully abstract for Hennessy Testing-equivalence on nets acting as refinement operators as well as operands. The semantics embodies the notions of deadlock, failures and divergences found in the Hoare/CSP and Hennessy Testing-equivalence theories, as well as some of the basic ideas of “pomset runs” and “causal” partial orders of Net theory.

A set of necessary conditions for a Petri net to be plain, pure and safe is given. Some applications of these conditions both in practice (for Petri net synthesis), and in theory (e.g., as part of a characterisation of the reachability graphs of live and safe marked graphs) are described.