Modeling of interval P-time Petri nets using dioid algebra

A PN-based approach to the high-level synthesis of digital systems

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.

Artificial neural networks (ANN's) are highly parallel and distributed computational structures that can learn from experience and perform inferences. Petri nets, on the other hand, provide an effective modeling framework for distributed systems. The basic concepts of Petri net are utilized to develop ANN-like multilayered Petri net architectures of distributed intelligence having learning ability. A Petri net model of single neuron is presented. A two-layer Petri net model-neural Petri net (NPN)-that uses this neuron model as a building block is described. A new class of Petri nets called the fuzzy neural Petri net (FNPN) is defined. The FNPN can be used for representing a fuzzy knowledge base and for fuzzy reasoning. Some application examples for the two Petri net based models are given. >

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 invited survey is to introduce Computer science/Petri nets specialists to the basic system level issues brought up by the development of Flexible Manufacturing and how Petri nets are used to aid the production engineers in their work. After some terminology concerning production engineering, the hierarchical decision and control level is briefly reviewed. Finally, the role and the presence of nets in CAE (Computer Aided Engineering) and in CAM (Computer Aided Manufacturing) for FMSs (Flexible Manufacturing Systems) are considered. From the design point of view, the use of nets have many advantages in modeling, qualitative analysis, performance evaluation and code generation. From the control of the plant perspective, scheduling on nets models, the coordination of the plant (global and partial) and the presence of nets in the local control level are discussed.Petri nets theory presents a relatively mature body, nevertheless efficient performance evaluation (even for P/T net models) and qualitative analysis of high-level net models still requires important developments. Moreover, the impression that the Petri net newcomer may have looking at the many variants of high-level-nets formalisms may initially produce some kind of rejection. In any case, it is our opinion that Petri nets appears as a key formalism to describe, analyze and implement the control of FMSs. The merging of Petri nets and knowledge based techniques seems to be very promising to deal with large complex discrete event dynamic systems such as FMSs.KeywordsFlexible Manufacture SystemDiscrete Event SystemProgrammable Logic ControllerComputer Integrate ManufactureMarked GraphThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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

It had been shown that Merlin's Time Petri Nets are a special case of Time Stream Petri Nets. In this paper, we show that there does not exist a time equivalence between both models. We extend first this result to the non equivalence of Timed Automata and Time Petri Nets and second to the non equivalence of Timed Link Petri Net and Timed Transition Petri Net.

Petri Nets (PNs) are an effective structure for modeling and analyzing asynchronous systems with concurrent and parallel activities. A Petri net models the static properties of a discrete event system concentrating on two basic concepts: events and conditions. Most of the theoretical work on Petri nets is a formal definition of Petri nets structures, which consist of a set of places, representing conditions, a set of transitions, representing events, an input function and an output function. For practical purposes, a graphical representation is more useful. Two types of nodes portray places and transitions. A circle is a place and a bar is a transition. There is no inherent measure of time in a classical Petri net. To approach time-based evaluation of system performances, Timed Petri Nets (TPNs) were introduced. Modeling the notion of time is not straightforward. There are several possibilities for introducing time in PNs, among them timed transitions and timed places. This paper reviews several published examples where Petri Nets were used in different circumstances such as estimating expected utilization of processing resources at steady state in open queueing networks, verifying computerized simulations and batch planning in textile industry.

The paper is a partial synthesis of the work that a team within the Faculty of Managerial and Technological Engineering has in the field of modeling and simulation of systems with Petri nets. The paper deals with three issues. The first part is Modeling and simulation of manufacturing systems with timed Petri nets. The first part presents the way in which the performances of some manufacturing systems are evaluated using timed Petri nets. The first example is a manufacturing system specific to the textile industry. The system has three production lines. In this case, the modeling with timed Petri nets allows the analysis of the operation of the flow lines and highlights the bottleneck. Another modeled manufacturing system is specific to a series production, more precisely it refers to the manufacture of gas cookers within a company from Oradea. The model with Petri nets also describes the supply sequences of the stocks of parts and subassemblies. The next modeled system is an automated manufacturing system for the packaging of detergents. The complexity of the Detergent Packing System and the high level of automation, require the use of efficient modeling and simulation methods to verify the validity of the solutions adopted. In this chapter is present the model of a robotic welding cell. The second part of the paper, the transition from timed Petri nets to hierarchical colored Petri nets, shows how Petri nets were developed for a robotic cell for metallographic analysis. The third part is dedicated to modeling with colored Petri nets timed with complex colors of the flexible manufacturing cell A007 within the Department of Industrial Engineering.

In this work, a novel hybrid modeling approach for HVAC control system design in Intelligent Buildings is introduced. In order to achieve building system integration, a characterization of HVAC system as hybrid is required. The proposed approach is a top-down modeling method based on Petri net. Starting from abstract models designed using the Production Flow Schema, Petri net based models are built by successive refinements. The discrete part of the system is modeled using Place-Transition Petri nets and the continuous part is modeled using differential equation systems. The interface between these two parts is provided by Differential Predicate Transition Petri nets.

The work undertaken in this thesis is about the integration of two well-known methodologies: Petri net (PN) model Ii ng/analysis of industrial production processes and Artificial Intelligence (AI) optimisation search techniques. The objective of this integration is to demonstrate its potential in solving a difficult and widely studied problem, the scheduling of Flexible Manufacturing Systems (FIVIS). This work builds on existing results that clearly show the convenience of PNs as a modelling tool for FIVIS. It addresses the problem of the integration of PN and Al based search methods. Whilst this is recognised as a potentially important approach to the scheduling of FIVIS there is a lack of any clear evidence that practical systems might be built. This thesis presents a novel scheduling methodology that takes forward the current state of the art in the area by: Firstly presenting a novel modelling procedure based on a new class of PN (cb-NETS) and a language to define the essential features of basic FIVIS, demonstrating that the inclusion of high level FIVIS constraints is straight forward. Secondly, we demonstrate that PN analysis is useful in reducing search complexity and presents two main results: a novel heuristic function based on PN analysis that is more efficient than existing methods and a novel reachability scheme that avoids futile exploration of candidate schedules. Thirdly a novel scheduling algorithm that overcomes the efficiency drawbacks of previous algorithms is presented. This algorithm satisfactorily overcomes the complexity issue while achieving very promising results in terms of optimality. Finally, this thesis presents a novel hybrid scheduler that demonstrates the convenience of the use of PN as a representation paradigm to support hybridisation between traditional OR methods, Al systematic search and stochastic optimisation algorithms. Initial results show that the approach is promising.

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.

Basic graph models of processes, such as Petri nets, have usually omitted the concept of time as a parameter. Time has been added to the Petri net model in two ways. The timed Petri net (TPN) uses a fixed number of discrete time intervals. The stochastic Petri net (SPN) uses an exponentially distributed random variable. In this paper, a discrete time stochastic Petri model is described. These discrete time SPN's fill the gap between TPN and normal SPN. However, the use of discrete time complicates the SPN model in that more than one transition may fire at a time step. Finally, an example of a live and bounded Petri net which has nonempty, disjoint, recurrent subsets of markings is given.

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.