Integrating Robotic Functions And Operator Supervision Using Petri Nets

Knowledge-based approach to Petri nets analysis

Petri net paradigm of computing is concerned discussing basic types of Petri net computers and their relations. We developed a technique of parametric specification of Petri nets, built of a few connected components which are repeated depending on a parameter or a set of parameters, and composition of software to generate automatically the corresponding models in a vivid graphical form. We construct explicitly a Petri net that is a strong computer of double exponent after R.J. Lipton. Its nondeterministic computation is represented by a Petri net reachability graph to which a successful branch belongs. Then we minimise and transform the net to obtain twice smaller construct than the original one. Moreover, the obtained net possesses such a marvellous property that addingto it four priority arcs makes it an exact (deterministic) computer having a single firable sequence only. Same as the Lipton’s net, the minimized net allows the proof that the Petri net reachability problem is exponential in space. Besides, it represents an example when simple transformations allow guessing the successful branch of a nondeterministic computation. The practical significance of the approach in applications consists in a state-of-art heuristic technique of solving some NP problems in polynomial time.

Modeling computer software, hardware, and other systems using Petri nets is discussed. The various analysis techniques and extension of Petri nets are considered. Problems in Petri net analysis techniques are examined, and analysis techniques that solve them are given.

We have proposed a high speed Petri net sequence controller for systems described in Petri nets. Its hardware is capable of checking whether a transition is fireable or not, although we did not take deadlocks into consideration. If a controller described in the Petri net has deadlocks, the proper methods to avoid them is to redesign the Petri net of the controller. But sometimes it is difficult to change the net or insert several places to avoid deadlocks, because there are no general methods to remove them. Thus we propose here a hardware to avoid deadlocks without changing the Petri net graph. The hardware unit inside the Petri net controller detects unsafe markings leading to deadlocks and prevents the current transition from being fired. The unit consists of three memory tables and some logical units to detect the matching of a current marking with those in the tables. It requests one memory cycle to check one only state. This idea can be used to avoid the undesired marking of the controlled object.

Probabilistic delay evaluation in combinational digital circuits by petri nets

In this paper we focused our attention on a particular hybrid PN model called FOHPN, that is based on the fluidification of discrete PNs, and whose main feature is that the instantaneous firing speed of continuous transitions keeps constant during each macroperiod. In the first part of the paper we discuss in detail the advantages of fluidification, and provide a brief survey of the most important formalisms within the hybrid PN framework. Finally, we showed how FOHPNs can be efficiently used to model SC, and how interesting optimization problems can be solved via numerical simulation, by simply solving on-line a certain number of LPPs.

Formal methods in Computer Science are a particular kind of mathematically-based techniques for the specification, development and verification of software and hardware systems. Among them, Petri Nets have been widely used because of their high expressive power and accurate description capabilities. On the other hand, Dynamical Systems theory has not been used for these purposes so far. In this paper we present the first use of Discrete Dynamical Systems under the aim to better analyze Concurrent Computing Systems. In order to do that, Petri Nets, PNs, are properly encoded into DDSs, so defining the corresponding Phase Space with its metric structure and the evolution operator of the system.

The article describes a part of our research in the area of (business) process modeling, analysis and execution. It describes the current state of process languages and standards. It concentrates on the process model interoperability and portability problems, caused because of huge number of process modeling standards, which often do not even target the same conceptual level of process modeling. It provides an idea how to bring together those standards, using process concepts mapping into Petri nets and incorporating the usage of process patterns. Transformation to strictly formal process languages has a potential to prove itself as a fair solution with the following advantages: the number of mappings among different process languages is reduced and the process model can be analyzed using proven Petri Net or general graph algorithms. Development of the approach is still in its early phase. Mapping rules to/from process patterns are neither strictly defined nor trivial, therefore, they will be the main focus of our future research.

Join-Free Petri nets, whose transitions have at most one input place, model without synchronizations while Choice-Free Petri nets, whose places have at most one output transition, model without conflicts. These classes respectively encompass the state machines (or S-systems) and the marked graphs (or T-systems).Whereas a structurally bounded and structurally live Petri net graph is said to be well-formed, a bounded and live Petri net is said to be well-behaved. Necessary and sufficient conditions for the well-formedness of Join-Free and Choice-Free nets have been known for some time, yet the behavioral properties of these classes are still not well understood. In particular efficient sufficient conditions for liveness have not been found until now. In this paper, we extend results on weighted T-systems to the class of weighted Petri nets and present transformations which preserve the feasible sequences of transitions and reduce the initial marking. We introduce a notion of balancing that makes possible the transformation of conservative into so-called 1-conservative systems while retaining the feasible transition sequences. This transformation leads to polynomial sufficient conditions of liveness for well-formed Join-Free and Choice-Free nets.

Petri net (PN) is an effective modeling and analysis tool for discrete event systems. By attaching a first-order logic predicate logic formula to a transition in a PN, a high-level Petri net named Logic Petri Net (LPN) is obtained. LPN has been proved to have equivalent modeling capability with inhibition Petri nets but keeps simpler net structures than the latter. It has the advantage of modeling the cooperative systems with the function to process batch and indeterminate resources. This paper proposes a vector computational method for LPN compositional analysis. It studies the composition of LPNs with the shared P-type subnets. Each logical expression is transformed into a unique disjunctive normal one and then into a unique set of vectors. A vector computational method is proposed such that the properties of the composition of the shared P-type subnets such as liveness, boundedness, and reversibility are verified. An E-commerce system with customers, merchants, and a third-party is constructed to illustrate the method. This paper can improve the state of the art in the theory of LPNs.

This paper shows how to use the Petri Net with Stacks (PNS-net) to express asynchronous concurrent distributed computing systems (DCS) which are based on the environment of loosely coupled computing systems, and puts forth method to detect types of DCS deadlocks such as Cycle Waiting, Hold and Wait, Exclusive access, etc. Then we can apply the algorithm that this paper narrates which actually changes PNS-net into production rules during the system-designing stages. By designing a diagnosis system for automatic detection of deadlocks in asynchronous concurrent distributed computing systems (ACDCS), the goal of this paper is to develop and approach for reducing the time and cost in the software development.

PSEE (Process-centered Software Engineering Environment) can manage and monitor software process. Software process modeling language is a core element in PSEE system. Due to the particularity and the complexity, software process model includes multi-views: activity view, product view and role view, which should be considered in modeling software process. Based on the similarity between multi-view software process modeling and object Petri nets, this paper proposes the MOPN-SP-net model which is a multi-view software process model based on multi-object Petri nets. The model includes twolevel models: system net and object net. A multi-view paradigm including activity views and product views is provided. Activity views are described by system nets and product views are described by object nets. MOPN-SP-net includes multi-views of software process model, which is characterized with clearer hierarchy, simpler structure, and more extendibility.

For Petri net models of flexible manufacturing systems,this work proposes a method to design liveness-enforcing supervisors based on complementary places.Firstly,a finite-capacity net珦Nis obtained from a given Petri net N by adding a capacity function K.Then,by increasing K to Kmax,the maximal reachability set of live finite-capacity net珦Nis computed and the complementary-place transformation is used to obtain the live system N′.Finally,an example of S3PR net is provided to compare with some other approaches proposed in prior work.Comparison results show that the liveness-enforcing supervisor obtained by the proposed method has simpler structure and more permissive behavior in some cases.Furthermore,another example of S3PGR2net shows that the proposed method can be applied to the general Petri nets.

ABSTRACTThis paper develops a concept of control transition equation (CTE) and the corresponding deadlock control algorithm (DCA) using control transitions (CTs) to eliminate deadlocks in Petri nets. By analysing the reachability graph (RG) of an original net with deadlocks, this DCA firstly find all deadlock markings (DMs) and then the corresponding CTs are solved on the basis of the proposed CTE. Secondly, a linear programming problem that can minimise the number of CTs is applied to these CTs. In addition, in order to furtherly simplify the structure of these CTs, the reconstruction of the necessarily added CTs is performed by a circulating sequence number method. Finally, a live controlled system with the simpler structure is obtained by adding the desired CTs to , which can reach the same number of states as the original plant model , i. e. live maximally reachable number. The proposed DCA is different from deadlock prevention policies using control places (CPs) in most existing literature and whose correctness and efficiency are verified via the theoretical analysis and the relevant several examples.

Petri nets provide a unifying and versatile framework for the synthesis and engineering of computational models of biochemical reaction networks and of gene regulatory networks. Starting with the basic definitions, we provide an introduction into the different classes of Petri nets that reinterpret a Petri net graph as a qualitative, stochastic, continuous, or hybrid model. Static and dynamic analysis in addition to simulative model checking provide a rich choice of methods for the analysis of the structure and dynamic behavior of Petri net models. Coloring of Petri nets of all classes is powerful for multiscale modeling and for the representation of location and space in reaction networks since it combines the concept of Petri nets with the computational mightiness of a programming language. In the context of the Petri net framework, we provide two most recently developed approaches to biomodel engineering, the database-assisted automatic composition and modification of Petri nets with the help of reusable, metadata-containing modules, and the automatic reconstruction of networks based on time series data sets. With all these features the framework provides multiple options for biomodel engineering in the context of systems and synthetic biology.