A Symbolic Algorithm for the Synthesis of Bounded Petri Nets

In this paper, the synthesis of bounded Petri nets from deterministic modal transition systems is shown to be undecidable. The proof is built from three components. First, it is shown that the problem of synthesising bounded Petri nets satisfying a given formula of the conjunctive nu-calculus (a suitable fragment of the mu-calculus) is undecidable. Then, an equivalence between deterministic modal transition systems and a language-based formalism called modal specifications is developed. Finally, the claim follows from a known equivalence between the conjunctive nu-calculus and modal specifications.

In this paper we present a survey on methods for the synthesis of Petri nets from behavioral descriptions given as languages. We consider place/transition Petri nets, elementary Petri nets and Petri nets with inhibitor arcs. For each net class we consider classical languages, step languages and partial languages as behavioral description. All methods are based on the notion of regions of languages. We identify two different types of regions and two different principles of computing from the set of regions of a language a finite Petri net generating this language. For finite or regular languages almost each combination of Petri net class, language type, region type and computation principle can be considered to compute such a net. Altogether, we present a framework for region-based synthesis of Petri nets from languages which integrates almost all known approaches and fills several remaining gaps in literature.

Pre-synthesis of Petri nets based on prime cycles and distance paths

Synthesising systems from behavioural specifications is an attractive way of constructing implementations which are correct-by-design and thus requiring no costly validation efforts. In this paper, systems are modelled by Petri nets and the behavioural specifications are provided in the form of step transition systems, where arcs are labelled by multisets of executed actions. We focus on the problem of synthesising Petri nets with whole-place operations and localities (wpol-nets), which are a class of Petri nets powerful enough to express a wide range of system behaviours, including inhibition of actions, resetting of local states, and locally maximal executions.

The elasticity principles have become one of the most important features of contemporary distributed systems. This novel paradigm has major consequences on Petri nets modeling. The problem is to decide whether an arbitrary Petri net satisfies the elasticity and how to make it elastic. The problem is solved by synthesis of Fractal Petri nets. Fractal Petri nets based on Iterated Algebraic System which makes possible elastic synthesis by incrementing or decrementing of original Petri net. One of the important tasks is recognition of a subnet which used as a pattern for elastic synthesis. For this purpose evolutionary classification of Petri nets based on subnets synthesis is introduced. And furthermore, algebraic operations replication and composition make elastic synthesis object-oriented. Control of the elasticity over the resources and system behavior is achieved with the use of patterns overlapping technique.

In this paper we present an algorithm to synthesize a finite unlabelled place/transition Petri net (p/t-net) from a possibly infinite partial language, which is given by a term over a finite set of labelled partial orders using operators for union, iteration, parallel composition and sequential composition. The synthesis algorithm is based on the theory of regions for partial languages presented in [17] and produces a p/t-net having minimal net behaviour including the given partial language. The algorithm uses linear programming techniques that were already successfully applied in [22] for the synthesis of p/t-nets from finite partial languages. Also, an equality test algorithm to check whether the behaviour of the synthesized p/t-net equals the given partial language is shown. Moreover, we present an implementation of the developed synthesis algorithm together with an example case study. Finally, a possible generalization of the presented term based representation of infinite partial languages is discussed.

Given a set of scenarios, we answer the question whether this set equals the set of all executions of a Petri net.Formally, scenarios are expressed by (isomorphism classes of) labelled partial orders (LPOs), also known as pomsets or partial words. An LPO is an execution of a Petri net if it is a sequentialization of an LPO generated by a process of the net. We propose a definition of regions for a set of LPOs, i.e for a partial language. Given a partial language of scenarios, we prove a necessary and sufficient condition (based on regions) for the partial language of scenarios to be the partial language of executions of a place/transition Petri net. Finally, we prove our notion of regions to be consistent with the notion of regions of trace languages.

Traffic lights are commonly used in the intersection in urban areas nowadays. In fact a network of the traffic lights regulating the urban vehicle can be viewed as a complex discrete-event system (DES). It is proved that Petri nets are one of the methodologies for modeling, analyzing and controlling on DES. A new approach via programmable logic controller (PLC) and Petri net synthesis is proposed in this paper. Firstly, we described the typical urban traffic lights control using Petri nets. Having compared with three methods for Petri nets realization, the best implementation method of the traffic lights control system was one which made with the PLC. The sequential function chart (SFC) of the PLC system is also given in the thesis. The result shown that the method has many advantages at improving flexibility and troubleshoots of system and reducing the difficulty in its realization.

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.

This paper addresses the problem of current-state opacity of discrete event systems (DES) modeled with Petri nets. A system is said to be current-state opaque if the intruder who only has partial observations on the system's behavior is never able to infer that the current state of the system is within a set of secret states. Based on the notion of basis markings, an efficient approach to verifying current-state opacity in bounded Petri nets is proposed, without computing the whole reachability set or exhaustively enumerating the set of markings consistent with the observation. An example showing the efficiency of the approach is presented.

This paper addresses the supervisor synthesis on the forbidden state problem, in which the forbidden markings cannot be easily expressed as linear inequality constraints using reported methods. The system to be controlled is modelled by bounded Petri nets with uncontrollable transitions. Through the analysis of the reverse net, we obtain the weakly forbidden markings in order to deal with uncontrollable transitions. By introducing a transformation function, which facilitates not only tracking the system state but also determining the control pattern, we propose a synthesis method to obtain the maximally permissive supervisor. The method need not analyze the reachability graph and the online computation has the complexity of polynomial times. In addition, for a special class of generalized Petri nets called the input dominant Petri nets, the synthesis method can be applied conveniently, as illustrated by an example in the reported literature.

We provide motivation for and then study the synthesis of Petri nets. Synthesis can avoid the state exploration problem by guaranteeing correctness for the Petri net. We propose conditions to be imposed on a synthesis shared pb-type subnet for systems specified in Petri nets that ensure the preservation of the liveness and boundedness structural properties. Specifically, we propose a group of sufficient conditions, or both sufficient and necessary conditions, for liveness preservation and boundedness preservation. Possible applications of this synthesis method are illustrated through an example in the form of a flexible manufacturing system. These results are useful for studying the static and dynamic properties of Petri nets for analysing the properties of large complex systems.

Regions of Petri nets with a/sync connections

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.

In this paper, we investigate transition systems of a class of Petri nets suitable for the modelling and behavioural analysis of globally asynchronous locally synchronous systems. The considered model of Elementary Net Systems with Localities (ENL-systems) is basically that of Elementary Net Systems (EN-systems) equipped with an explicit notion of locality. Each locality identifies a distinct set of events which may only be executed synchronously, i.e., in a maximally concurrent manner. For this reason, the overall behaviour of an ENL-system cannot be represented by an interleaved transition system, with arcs being labelled by single events, but rather by a suitable notion of a step transition system, with arcs being labelled by sets of events executed concurrently.We completely characterise transition systems which can be generated by Elementary Net Systems with Localities under their intended concurrency semantics. In developing a suitable characterisation, we follow the standard approach in which key relationships between a Petri net and its transition system are established via the regions of the latter defined as specific sets of states of the transition system. We argue that this definition is insufficient for the class of transition systems of ENL-systems, and then augment the standard notion of a region with some additional information, leading to the notion of a region with explicit input and output events (or io-region).We define, and show consistency of, two behaviour preserving translations between ENL-systems and their transition systems. As a result, we provide a solution to the synthesis problem of Elementary Net Systems with Localities, which consists in constructing an ENL-system for a given transition system in such a way that the transition system of the former is isomorphic to the latter.KeywordsTheory of concurrencyPetri netselementary net systemslocalitiesanalysis and synthesisstep sequence semanticsstructure and behaviour of netstheory of regionstransition systems