Interpretation Of Petri Nets Research Articles

Token Multiplicity in Reversing Petri Nets Under the Individual Token Interpretation

Reversing Petri nets (RPNs) have recently been proposed as a net-basedapproach to model causal and out-of-causal order reversibility. They are based on the notion of individual tokens that can be connected together via bonds. In this paper we extend RPNs by allowing multiple tokens of the same type to exist within a net based on the individual token interpretation of Petri nets. According to this interpretation, tokens of the same type are distinguished via their causal path. We develop a causal semantics of the model and we prove that the expressive power of RPNs with multiple tokens is equivalent to that of RPNs with single tokens by establishing an isomporphism between the Labelled Transition Systems (LTSs) capturing the reachable parts of the respective RPN models.

A collective interpretation semantics for reversing Petri nets

Reversing Petri nets (RPNs) have recently been proposed as a net-based approach to model causal and out-of-causal order reversibility. They are based on the notion of individual tokens that can be connected together via bonds. In this paper we extend RPNs by allowing multiple tokens of the same type to exist within a net and we implement a notion of local reversibility for the model based on the collective token interpretation of Petri nets. The resulting framework allows us to model a form of out-of-causal-order reversibility, a type of reversibility that arises most notably in biological systems. Furthermore, it is lightweight in the sense that it requires no global control and no history needs to be preserved. Furthermore, we provide a mechanism for controlling reversibility by associating transitions with conditions, which guard their execution. We demonstrate the usefulness of the framework by modelling the functioning of the sodium-potassium pump, a system where transition execution is governed by activation conditions and featuring reversible behaviour.

CAUSAL REVERSIBILITY IN INDIVIDUAL TOKEN INTERPRETATION OF PETRI NETS

Causal reversibility in concurrent systems means that events that the origin of other events can only be undone after undoing of its consequences. In opposite to backtracking, the events which are independent of each other can be reversed in an arbitrary order, in the other words, we have flexible reversibility w.r.t the causality relation. An implementation of Individual token interpretation ofPetri Nets (IPNs) was been proposed by Rob Van Glabbeek et al, the present paper investigates into a study of causal reversibility within IPNs. Given N be an IPN, by adding an intuitive firing rule to undo transitions according to the causality relation, the coherence of N is assured, i.e., the set of all reachable states of N in the reversible version and that of the original one are identical. Furthermore, reversibility in N is flexible and their initial state can be accessible in reverse from any state. In this paper an approach for controllingcausal-reversibility within IPNs is proposed.

CONCEPTUAL REPRESENTATIONS AND MODIFICATIONS OF PETRI NETS FOR APPLICATIONS IN THE AREA OF SYNTHESIS OF A FUNCTIONAL ARCHITECTURE OF DISTRIBUTED COMPUTATIONAL SYSTEMS WITH VARIABLE STRUCTURE

Background. The object of the research is the functional architecture of distributed computing systems with a variable (reconfigurable) structure characteristic of hybrid systems of cloud-network (grid) type. Despite the fact that Petri nets have long been studied both theoretically and practically, the methods of their interpretation continue to develop intensively. At present, the problem of embedding Petri nets in the architecture of distributed network applications used to implement global computing in modern mixed cloud, grid and cluster systems has not been sufficiently studied. It is shown that in modern studies, Petri nets are used mainly in the simulation of discrete systems and processes, and not as the basis for formalized specifications in the development of distributed applications. In this regard, the interpretation of Petri nets in applications to the functional architecture of distributed computing systems with a variable structure based on the network software of the intermediate class (middleware class) is relevant. The aim of the work was the integration of graphical representations of conceptual graphs, semantic networks, scenarios and Petri nets, which made it possible to create effective tools with graphical support for designing a functional architecture of distributed computing systems with a variable structure and, in particular, a cloudy architecture of the NCaaSoD type - Network Computing as a Service on Demand (network computing as a cloud service at the request of the user).Materials and methods. The conceptual models of distributed processes that are a graphical interpretation of the first-order predicate calculus are used. Conceptual graphs for distributed Petri nets of mixed type have been proposed, which allow describing computation processes in global computational networks with a view to their subsequent implementation. Results. Based on the integration of graphical representations of conceptual graphs, semantic networks, scenarios and Petri nets, conceptual representations of distributed reconfigurable Petri nets are proposed, allowing them to be directly integrated into the architecture of the computer network.Results. New conceptual-behavioral models based on conceptual graphs of distributed Petri nets have been proposed to determine the system and functional architectures of distributed computing systems with a variable structure provided to the user as a hybrid cloud-based network service; these models are distinguished by the possibility of operational reconfiguration and immediate execution.Conclusion. A method was proposed and formalized for embedding conceptual Petri nets into the architecture of cloud-networked computer systems such as NCaaSoD — network (cloud) computing as a service organized at the user's request. The rules for obtaining relations of connectivity between the positions and transitions of the Petri net, placed on the nodes of the physical computer network, are proposed.

Petri nets are dioids: a new algebraic foundation for non-deterministic net theory

In a seminal paper Montanari and Meseguer have shown that an algebraic interpretation of Petri nets in terms of commutative monoids can be used to provide an elegant characterisation of the deterministic computations of a net, accounting for their sequential and parallel composition. A smoother and more complete theory for deterministic computations has been later developed by relying on the concept of pre-net, a variation of Petri nets with a non-commutative flavor. This paper shows that, along the same lines, by adding an (idempotent) operation and thus considering dioids (idempotent semirings) rather than just monoids, one can faithfully characterise the non-deterministic computations of a net.

Methods of dynamic verification of the code based on the interpretation of Petri nets

One of the topical problems in the development of secure applications is the improvement of the quality of the software systems with parallel-sequential code. The verification of a software project is able to solve this problem, subject to the construction of adequate models of functioning of applications and the use of qualitative methods of verification of parallel-sequential programming models. The article considers the methods of static and dynamic verification of applications. The structure of the model for verification was proposed to be build on the basis of an intermediate model that is a complete parse tree. The working model was formed as the control Petri net (SN) with stochastic elements that allowed simulating the functioning of application under different time and communication conditions, and allowed static and dynamic analysis of critical situations. While constructing the model we have implemented the control function of the verifier, which consisted in analysis of the effects of correction of defects in the code, which would help achieve the control of the verification of applications. The article contains the example of the practical implementation of these methods - a verification of the applications written in C ++.

A Petri Net Interpretation of Open Reconfigurable Systems

We present a Petri net interpretation of the pi-graphs-a graphical variant of the picalculus where recursion and replication are replaced by iteration. The concise and syntax-driven translation can be used to reason in Petri net terms about open reconfigurable systems. We demonstrate that the pi-graphs and their translated high-level Petri nets agree at the semantic level. In consequence, existing results on pi-graphs naturally extend to the translated Petri nets, most notably a guarantee of finiteness by construction.

Combining Soft Linear Logic and Spatio-temporal Operators

A new logic, spatio-temporal soft linear logic, which has soft linear exponential, linear exponential and spatio-temporal operators, is introduced as a sequent calculus. A Petri net interpretation and an informational interpretation for this logic are given by using simple complete semantics. By using this logic and these interpretations, various kinds of spatio-temporal and resource-sensitive reasoning can be expressed.

PETRI NETS AS A TOOL FOR MINE SIMULATION

Lately high-level Petri nets have found broadening applications to simulate compound systems in decision-making, informatics, and manufacturing. A process is reflected as a movement of tokens across logical transitions with time delays in places of net. The properties and computer interpretation of Petri nets are described. A complete mining system can be formed from standard components that are presented as Petri nets. Petri nets for a longwalling, driving, mine-wide conveyor net, conveyor-locomotive transport, and robotics-based mining had been constructed. They have been used to solve a number of practical problems, such as coordination of a cutting and supporting, designing and dispatching of compound transport systems, choice of loading strategy for LHD's, interaction between robots and mining machines, and design of mining robots.

Efficient computerized Petri net approach for the enumeration of the sets of path identifiers for reliability analysis of broadcasting networks

An efficient Petri net approach for enumerating the sets of path identifiers for the reliability analysis of broadcasting networks is presented. The sets of path identifiers are enumerated with the help of a place-to-transilion incident matrix of the Petri net model of Ihe given network. The reachability, marking and firing concepts of Petri nets are used to give a Petri net interpretation to certain properties of the network. The proposed method is applicable to ST-connectivity, SKT-connectivity and SAT-connectivity problems. The sets of path identifiers are generated in ascending order of cardinality which is one of the basic requirements for efficiency in most of the techniques available for obtaining the symbolic and numerical system reliability expressions. The developed algorithm has been programmed in FOR-TRAN-77 and tested on various types of data. The proposed method directly obtains the sels of path identifiers for SKT- and SAT-connectivity problems without the necessity of generating the ST-minimal path sets. In comparison to the previously published approach, the algorithm is conceptually simpler and requires less computer time and memory space. Examples have been provided to demonstrate the effectiveness of the method. A comparison of CPU time and memory requirement of the present method with an existing method has also been given.

Determination of path identifiers for reliability analysis of a broadcasting network using Petri nets

A Petri net approach for determination of the sets of path identifiers for reliability analysis of a broadcasting network is presented. The firing concept of Petri nets is exploited to give a Petri net interpretation to certain properties of the network. The dynamic behaviour of the system under study is represented in the form of token movements within the model. The various entities of Petri nets are assigned an appropriate interpretation for studying the behaviour of the system at different levels. Corresponding to the source node and each of the terminal nodes, a vector, representing the state of the Petri net interpreted model, is defined by assuming a token initially at the source place and finally at one of the terminal places. The reachability and marking concepts are then used to determine all success states of the system. The developed algorithm has been coded into FORTRAN-77 and the complete package is available. The proposed technique is extremely simple as it uses only vector additions on the columns of the place-to-transition incident matrix.

Determination of path identifiers for reliability analysis of a broadcasting network using Petri nets

A Petri net approach for determination of the sets of path identifiers for reliability analysis of a broadcasting network is presented. The firing concept of Petri nets is exploited to give a Petri net interpretation to certain properties of the network. The dynamic behaviour of the system under study is represented in the form of token movements within the model. The various entities of Petri nets are assigned an appropriate interpretation for studying the behaviour of the system at different levels. Corresponding to the source node and each of the terminal nodes, a vector, representing the state of the Petri net interpreted model, is defined by assuming a token initially at the source place and finally at one of the terminal places. The reachability and marking concepts are then used to determine all success states of the system. The developed algorithm has been coded into FORTRAN-77 and the complete package is available. The proposed technique is extremely simple as it uses only vector additions on the columns of the place-to-transition incident matrix.

Simplification of Boolean functions through petri nets

A technique exploiting the modern concepts of Petri nets for simplification of Boolean functions is proposed. The firing concept of Petri nets has been utilized to give a Petri net interpretation to certain properties of switching algebra. These Petri net interpreted properties are then used for the simplification process. Unlike the existing method, the proposed technique does not require the functions to be expressed explicitly in a canonical form. This alleviates the computational efforts. It is simple and amenable for computer programming implementation.