Bounded Petri Net Synthesis from Modal Transition Systems is Undecidable.

This paper presents an algorithm for the synthesis of bounded Petri nets from transition systems. A bounded Petri net is always provided in case it exists. Otherwise, the events are split into several transitions to guarantee the synthesis of a Petri net with bisimilar behavior. The algorithm uses symbolic representations of multisets of states to efficiently generate all the minimal regions. The algorithm has been implemented in a tool. Experimental results show a significant net reduction when compared with approaches for the synthesis of safe Petri nets.

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.

Modal Transition System (MTS) is a well studied formalism for partial model specification. It allows a modeller to distinguish between required, prohibited and possible transitions. Disjunctive MTS (DMTS) is an extension of MTS that has been getting attention in recent years. A key concept for (D)MTS is refinement, supporting a development process where abstract specifications are gradually refined into more concrete ones. Refinement comes in different flavours: strong, observational (where \(\tau \)-labelled transitions are taken into account), and alphabet (allowing the comparison of models defined on different alphabets). Another important operation on (D)MTS is that of merge: given two models M and N, their merge is a model P which refines both M and N, and which is the least refined one.

Modal transition systems provide a behavioral and compositional specification formalism for reactive systems. We survey two extensions of modal transition systems: parametric modal transition systems for specifications with parameters, and weighted modal transition systems for quantitative specifications.

Modal transition systems are an elegant way to formalise the design process of a system through refinement and composition. Here we propose to adapt this methodology to asynchronous composition via Petri nets. The Petri nets that we consider have distinguished labels for inputs, outputs, internal communications and silent actions and “must” and “may” modalities for transitions. The input/output labels show the interaction capabilities of a net to the outside used to build larger nets by asynchronous composition via communication channels. The modalities express constraints for Petri net refinement taking into account observational abstraction from silent transitions. Modal I/O-Petri nets are equipped with a modal transition system semantics. We show that refinement is preserved by asynchronous composition and by hiding of communication channels. We study compatibility properties which express communication requirements for composed systems and we show that these properties are decidable, they are preserved in larger contexts and also by modal refinement. On this basis we propose a methodology for the specification of distributed systems in terms of modal I/O-Petri nets which supports incremental design, encapsulation of components, stepwise refinement and independent implementability.KeywordsCommunication PropertySilent TransitionConsuming PropertyModal RefinementInput LabelThese 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.

With the aim to preserve deadlock freedom, we define a new refinement relation for modal transition systems (MTS), using an MTS-specific variant of testing in the sense of De Nicola and Hennessy. We characterize this refinement with a kind of failure semantics, and we show that it 'supports itself' e.g. in the sense of thoroughness -- in contrast to the standard modal refinement. We present a conjunction operator w.r.t. our new refinement, this operator is very different from others found in the literature, and it demonstrates that the conjunction of two MTSs is an MTS -- again in contrast to the case of modal refinement. Finally, we also consider a may-testing approach.

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.

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.

Gamma titanium aluminide (γ-TiAl) based alloys are very interesting materials for structural applications at elevated temperatures owing to the combination of high specific strength, good oxidation, creep and fatigue resistance. However, their relatively poor ductility and fracture toughness remain important obstacles for their industrial applications in engineering components. The mechanical properties of these alloys, namely the poor room temperature ductility, as well as the yield stress, creep and fracture resistance, can be significantly improved by controlling the microstructure. These alloys undergo solid state phase transformations upon cooling from the high temperature α phase, which results in formation of different types of microstructures depending on the cooling conditions and the alloy composition. Low and moderate cooling rates lead to the precipitation of the γ phase as parallel plates within the α matrix, followed by the α → α2 ordering reaction. As a result of this transformation, the characteristic lamellar structure of TiAl is produced. Rapid cooling leads to a massive transformation from α to γ. It has been shown that the massive microstructure can be used as a precursor to obtain a refined microstructure through a subsequent tempering in the α + γ phase field. However, obtaining a fully massive microstructure at all depths in a component can be difficult to achieve. Numerical simulation of microstructure formation can be used as a tool to anticipate the microstructure distribution in a component depending on the local chemistry and cooling conditions. The main objective of this work was to develop microstructure models describing the formation of the massive and lamellar microstructures. Two distinct modeling approaches have been used. The first approach is a deterministic model having for objective to predict the microstructure distribution in a cast and heat treated component. The model was designed to be integrated into a FEM or FDM heat flow solver in order to calculate microstructural quantities such as the proportion of phases and lamellar spacings at each nodal point of the mesh. The modeling approach is based on a combination of nucleation and growth laws which take into account the specific mechanisms of each phase transformation. Nucleation of massive and lamellar γ is described with classical nucleation theory, accounting for the fact that nuclei are formed predominantly at α/α grain boundaries. Growth of the massive γ grains is based on theory for interface-controlled reactions. A modified Zener model is used to calculate the thickening rate of the lamellar γ precipitates. The model incorporates the effect of particle impingement and coverage of the nucleation sites by the growing phases. The driving pressures of the phase transformations are obtained from Thermo-Calc based on the actual temperature and matrix composition. The deterministic approach was used to calculate CCT diagrams and lamellar spacings, which showed to be in good agreement with experimental data obtained from dedicated heat treatment experiments and from the literature. The model permitted investigating the influence of cooling rate, alloy chemistry and average α grain size upon the amount of massive γ and the average thickness and spacing of the lamellae. In particular, it indicated that the Al depletion of the α phase during lamellar precipitation seems to play an important role in the suppression of the massive transformation at moderate cooling rate and in the large lamellar spacings observed at low cooling rate. It was also found that Nb additions enhance the formation of massive γ by lowering the lamellar transformation temperature, increasing the T0 temperature and slowing down the lamellar growth due to the low diffusivity of Nb. The second approach was a cellular automaton (CA) model, which was used to describe the formation of the lamellar microstructure on the scale of a few microns. The objective of this approach was to make a direct description of the growth of a precipitate by an interfacial ledge mechanism, and then to evaluate whether the simplifications made in the deterministic model regarding this mechanism are appropriate. The modelling approach is based on the resolution of the diffusion equations in the α and γ phases. The ledge structure at the α/γ interface is described by introducing different types of cells in the CA grid. The CA model was used to describe the formation of the lamellar microstructure at isothermal conditions and at various cooling rates. The thickening kinetics of the lamellae, the lamellar spacings and the overall kinetics of the transformation were calculated with this approach and were compared with the results obtained with the deterministic model. It was found first that the thickening kinetics of the lamellae calculated with the deterministic model are slower than those calculated with the CA model. It was established that the method used in the deterministic model to account for the growth by a ledge mechanism always leads to a growth exponent of 0.5, which is characteristic of diffusion controlled reactions. In contrast, the CA approach yields growth exponents that are comprised between 0.5 and 1, as it is expected for growth in a mixed diffusion/interface controlled mode. The incorporation of a kinetic undercooling term into the deterministic model was found to be an appropriate correction. A good agreement was finally obtained in terms of lamellar spacings and overall kinetics. The underestimated thickening kinetics of the deterministic model was observed to be partly compensated by a higher nucleation rate at the beginning of the transformation. The overall kinetics of the lamellar transformation calculated with the deterministic model was found to be sufficiently accurate to correctly predict the competition between the lamellar and massive microstructures.

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.

Security of distributed control systems is affected by the presence of information leaks, which permit to external intruders to infer the state of the system itself. Noninterference deals with the absence of such leak paths in a dynamic system modeled as discrete-event system. For a system that presents information leaks, a supervisory control strategy to enforce noninterference is proposed in this article. The approach is based on the solution of optimization problems on a Petri net model of the system under investigation. The effectiveness of the proposed enforcement strategy is shown by means of illustrative examples.

State-Partition-Based Control of Discrete Event Systems for Enforcement of Regular Language Specifications