Properties of Plain, Pure, and Safe Petri Nets

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.

The aim of this work is the modeling and verification of concurrent systems subject to dynamic changes using extensions of Petri nets. We begin by introducing the notion of net rewriting system. In a net rewriting system, a system configuration is described as a Petri net and a change in configuration is described as a graph rewriting rule. We show that net rewriting systems are Turing powerful, that is, the basic decidable properties of Petri nets are lost and, thus, automatic verification in not possible for this class. A subclass of net rewriting systems are reconfigurable Petri nets. In a reconfigurable Petri net, a change in configuration amounts to the modification of the flow relations of the places in the domain of the involved rule according to this rule, independently of the context in which this rewriting applies. We show that reconfigurable Petri nets are formally equivalent to Petri nets. This equivalence ensures that all the fundamental properties of Petri nets are still decidable for reconfigurable Petri nets and this model is thus amenable to automatic verification tools. Therefore, the expressiveness of both models is the same, but, with reconfigurable Petri nets, we can easily and directly model systems that change their structure dynamically.

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.

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

We use the by now well established setting of modal semirings to derive a modal algebra for Petri nets. It is based on a relation-algebraic calculus for separation logic that enables calculations of properties in a pointfree fashion and at an abstract level. Basically, we start from an earlier logical approach to Petri nets that in particular uses modal box and diamond operators for stating properties about the state space of such a net. We provide relational translations of the logical formulas which further allow the characterisation of general behaviour of transitions in an algebraic fashion. From the relational structure an algebra for frequently used properties of Petri nets is derived. In particular, we give connections to typical used assertion classes of separation logic. Moreover, we demonstrate applicability of the algebraic approach by calculations concerning a standard example of a mutex net.

This paper presents a new Web based Petri net Editor employing AJAX principles to allow the interactive design and edition of Petri net models using standard Web browsers. The editor includes an integrated plug-in architecture to simplify the addition of generic net operations without requiring the manipulation of internal editor data-structures. IOPT-nets are a non-autonomous Petri net class targeting the model-based development of embedded system controllers and combine the well know properties of Petri nets with input and output signals and events to establish the communication of controllers with the external world. The editor is a part of the IOPT-tools Web service that also contains model-checking and automatic code-generation tools, supporting a complete model-based development work-flow, starting from model design to the final controller code generation. All tools are available at the research group Web page (http://gres.uninova.pt).

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.

Petri nets are used as models of asynchronous concurrent systems. The underlying structure of a Petri net is a bipartite digraph. Many properties of Petri nets and the systems they model can be described in graph theoretic terms. These include the notions of deadlocks and traps. In this paper we consider these properties by restricting attention to some special classes of Petri nets including simple, complete, and free-choice Petri nets.

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.

Petrinets are the suitable tool for modeling and analysis of discrete event systems. The effective methods of analyzing the discrete event systems (DES) are exhibited by Petri nets. The entire structure of the system is mathematically expressed using Petrinets and also all the properties are analysed by different methods. The properties of Petrinets are different in various systems, a Flexible Manufacturing System (FMS) requires production activities in which raw materials, energy, labour, and equipment are combined together in the modification process for the production of good quality goods.” The word “flexible” explains the capability of the system to relate productively to make changes in the system. These changes can be internal failure of the system or classification problems such as a sample or external changes in the structure of the model as well as demand for the process. The inherent limitations such as undecidable properties, complexity in checking, automatic verification of the modeled system are existing in FMS. This paper explains a study on FMS using Petri net reduction. A PN underlies event structures with casuality and compatibility relations. Partial order methods and reduction methods reduce the complexity of constructing the reachability graph. The determination of PN system through reduction methods in recent years focused by many researchers. The significance of reduction methods are highlighted to execute the faster analysis of a system. Instead of coverability trees and the graphical representation the incidence matrix of the PNs are used for the reduction methods. Reduction methods are used to simplify large scale PNs into “equivalent” smaller nets. Boundedness, liveness, simplification of implicit places, shared resources and elimination of self-loops are checked though equivalent smaller nets. The structure of FMS is preserved.

We consider Nested Petri nets (NP-nets), i.e. Petri nets in which tokens can be Petri nets themselves. To increase flexibility and give tools for modeling adaptive processes we extend this formalism by allowing operations on net tokens. We prove decidability of some crucial for verification problems and thus show that, in spite of very flexible structure, NP-nets maintain "good" properties of ordinary Petri nets.

The dynamic behavior of concurrent systems can be modeled and analyzed using Petri nets. Many approaches have been proposed to analyze the properties of Petri nets. Among them, reachability analysis is a fundamental method for studying the dynamic properties of Petri nets. However, state space explosion has obstructed its applicability for analyzing large-scale systems. This paper presents a new method to attack state space explosion based on the concept of compositional verification. The strength of our method is in preserving the global information of Petri nets and a set of more effective condensation rules especially for tightly coupled modules (subnets). The current version of our method provides an efficient analysis for detecting deadlock states. An extension of our method for detecting reachable markings is also described.

The design process of control programs that drive the operation of new generation manufacturing systems has to respond quickly to the changes of a evolutionary market. The improvement towards a completely automated design process is actually arising from the field of artificial intelligence. This work presents an application of artificial intelligence planning techniques for the automatic generation of control programs for a manufacturing system expressed as safe and live Petri nets. This system allows for a fast generation of sound results, reducing the cost and duration of the design and development phase of control programs.

On Selected Properties of Uninorm Petri Nets and Their Application in Modeling Knowledge-Based Systems