Abstract: This paper introduces a novel approach to the real-time decision-making in service-oriented manufacturing systems, addressing the myopia problem usually presented in such systems. The proposed decision method considers the knowledge extracted from the **Petri** **nets** models used to describe the services process behavior, mainly the T-invariants, combined with a multi-criteria function customized according to the system’s particularities and strategies. An experimental laboratorial case study was used to demonstrate the applicability of the proposed real-time decision-making approach in service-oriented manufacturing systems, considering some productivity and energy efficiency criteria.

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orchestration engines, can be defined using different methods [5], namely the Business Process Execution Language (BPEL) [6] and the **Petri** **nets** formalism (see the work of Hamadi and Benatallah [7] and Deng et al. [8]). In this work, the selected modeling language is **Petri** **nets** taking advantage of its powerful mathematical foundation that will support, among others, the analysis and validation during the design phase and the decision making for conflict resolution.

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Abstract – Biological Regulatory Networks (BRNs) depicts the basic interactions in between various nodes in all biological systems. Inherently, all chemical and biological actions are governed by continuous functions, however, they have been modeled in discrete domain through Rene Thomas' Formalism. While the knowledge of steady states is sufficiently captured by this formalism, the dynamical properties of the changes taking place are not described. Hybrid Modeling was introduced to cover this aspect as it associated a range of delays with the changes in expression levels of various genes and hence insight in the dynamical behaviour of BRNs was achieved. However, the chemical reactions as well as the biological interactions are all stochastic in nature and could therefore assume any rate of change within the range of delays determined through Hybrid Modeling. Therefore, we have extended the Hybrid Modeling framework to Stochastic Modeling using an improved and simplified approach for conversion of BRN to Stochastic **Petri** **Nets** (SPNs) in which the random delay in firing of the transitions aptly captures the stochastic behaviour of changes in expression levels of genes. The proposed framework has been applied to the mucus production in Pseudomonas Aeruginosa BRN and results given by the Stochastic **Petri** **Nets** are in agreement with the Hybrid Modeling results from which establishes the accuracy of this approach as well as provide more insight in the dynamical behaviour of BRNs through simulation.

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The class of finite-net Multi-CCS processes represents a language for describing finite P/T **nets**. This is not the only language expressing P/T **nets**: the first (and only other) one is Mayr’s PRS [15], which however is rather far from a typical process algebra as its basic building blocks are rewrite rules (instead of actions) and, for instance, it does not contain any scope operator like restriction or hiding. We think the language we have identified can be used in order to cross-fertilize the areas of process calculi and **Petri** **nets**. In one direction, it opens, e.g., the problem of finding axiomatizations of **Petri** **nets** behaviours. For instance, net isomorphism induces a lot of equations over Multi-CCS terms. Just to mention a few, parallel composition is associative, commutative with 0 as neutral element, terms that differ only for alpha-conversion of bound names are identified, the sum operator is associative, commutative and, if the sequential term p is not 0, then also p + 0 = p and p + p = p hold. Even if the problem of finding a complete set of axioms characterizing net isomorphism is probably out-of-reach, nonetheless, the axioms we have identified are interesting as they include those forming the structural congruence for CCS [20], hence validating their use. On the other direction, **Petri** net theory can offer a lot of support to process algebra. Some useful properties are decidable for finite P/T **nets** (e.g., reachability, liveness, coverability – see e.g., [22] – model-checking of linear time µ-calculus formulae [7]) and so also the (infinite-state systems of) finite-net Multi-CCS processes can be checked against these properties. Moreover, P/T **nets** are equipped with non-interleaving semantics, where parallel composition is not reduced to sum and prefixing, and these semantics can be used fruitfully to check causality-based properties, useful, e.g., in error recovery.

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Time **Petri** **nets** [30] are one among the important formal models widely used to specify and verify real-time systems. They are characterized by their expressive power of parallelism and concurrency, and the conciseness of the models. In addition, the efficient analysis methods proposed by [10] have contributed to their wide use. Adding priorities to TPN (PrTPN) increases their expressiveness [2] and [9]. Since we address the testing of reactive systems, we associate a label of an alphabet of actions with each transition (LPrTPN). A label is an input or an output or an internal action.

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history of the application of both groups of languages to the workflow area has ap- proximately the same age. Although the genesis of **Petri** **nets** ascends to 1962, with the PhD dissertation of Carl Adam **Petri** [**Petri**, 1962], according to [Aalst et al., 2003] the use of variants of **Petri** **nets** to model office proceedings (in what can be considered the precursors of the WMSs – the so called “Office Information Systems”) took place only in the seventies, with the initiative of researchers like Clarence (Skip) Ellis [Ellis, 1979], Anatol Holt [Holt, 1985] and Michael Zisman [Zisman, 1977]. According to [Best and Koutny, 2004], the first ideas of process algebras were introduced in the same age by Tony Hoare [Hoare, 1978] and Robin Milner [Milner, 1980]. As also mentioned by [Best and Koutny, 2004], the relations between both groups of languages have been studied during their development. Possibly motivated by commercial interests, some apologists of one, or the other, group of languages have incurred in exaggerated appre- ciations of the qualities of their preferred languages, as commented in an unpublished paper [Aalst, 2003], about the relative strengths and weaknesses of process algebras and **Petri** **nets**, with a clear conclusion in favor of **Petri** **nets**.

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The seeds of castor bean have high energetic value and, when they are crushed, culminate in the formation of oil and mass residuals. The castor bean oil has several industrial applications, such as the production of biodiesel, while the mass residuals can be employed in the production of animal ration with a high rate of lipids and proteins, as well as compost. Conjointly with the obtaining of oil and mass residuals, it can be obtained from the castor bean cellulose (originated from its stalk and root structure) and silk (originated from the feeding of silkworms with its leaves). The castor bean agribusiness is constituted of a complex supply chain, involving several inputs, products and sub products (ARRUDA and MENDES, 2006). In this way, efforts directed to improve the performance of this chain become necessary in order to maximize its benefit/cost ratio. The objective of this paper is to report the conception and application of a simulation and supervisory control model, based on colored **Petri** **nets**, which allows the coordination of activities in the context of Castor Bean Biodiesel Supply Chain (CBBSC), aiming to guarantee its effectiveness. The paper is divided in five sections included this one: in the second section, the CBBSC is reported; in the third section, concepts about supervisory control, **Petri** **nets** and a new method of synthesis of supervisors denominated Constraints of Control on Decomposed Colors (CCDC) are presented; in the fourth section, a proposal about architecture of supervisory control for logistical systems and the modeling of CBBSC are described – a proposal about control of such system and the evaluation of its performance; finally, in the

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Decision points, alternative paths in a control logic topology, and other kind of sequential or parallel mutual exclusion relationships [5] that appear in the system to be orchestrated, are explicitly modelled by transitions in conflict by the **Petri** **nets**, the same way that web services related functions are able to figure out as transitions and places in **Petri** **nets**. Such features require the intervention of decision mechanisms. This is especially valid when considering that automation systems are inherited dynamically and not fully predictable; sometimes there are unexpected circumstances that a simple executed **Petri** net cannot handle: operation's delay and cancelling, synchronization among individual

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The well production test is a necessary process to measure the production potential of the exploration fields. The frequency of the production test is subject to inspection by the National Petroleum, Natural Gas and Biofuels Agency (ANP), which is one of the activities of the oil industry that carries out the royalties and the collection of taxes. By using resources of the company studied, the production test is a critical process that is not always performed satisfactorily. They were invited to develop a system of discrete event concepts, using **Petri** **nets**, in order to understand the behavior of the process in question, and to establish the basis for the investigation of future simulation applications. To achieve these objectives, it is necessary that the components of the system and their respective components with the phases of the test. Next, a flow chart was elaborated, necessary to develop the model in **Petri** **nets**, which are such steps. The **Petri** net was used in order to prove the consistency of the model developed. The various forms consisted of: reducing through simplification of the network; verification of accessible markings; ("vivacity", "limitability" and "verifiability"). The base **Petri** net was, for example, that which is no longer a network as properties, as this distribution capacity for a representation of the real system.

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In timed transitions with deterministic time delay there is a constant time delay associated with the transition. This type of transitions allows modelling discrete processes and changing the qualitative behaviour of the model with respect to the untimed **Petri** **nets** (Marsan and Chiola, 1986). On the other hand, timed transitions with stochastic time delay are defined to be random variables with given sta- tistical distributions. This type of transitions is very useful to model random processes, and the firing rate can be defined from different probabilistic distributions (Dugan et al., 1984; Marsan and Chiola, 1986). Immediate transitions are associated with the original concept proposed by **Petri** (1962) where, by definition, the firing delay is equal to zero. This transitions are used to represent logical control or an activity whose delay is negligible when compared with those associated with timed transitions (Marsan et al., 1984; Murata, 1989). Continuous timed transitions are associated with CTPN and are used to model continuous systems (Alla and David, 1998). Finally, reset transitions have associated a list of places and number of tokens that each place will contain after the **Petri** net resets. A reset action can be performed using the original concept of PN but would require a large number of transi- tions and places to be added to the model that would increase the size and complexity, confusing the engineering process that is being modelled (Andrews, 2013; Le and Andrews, 2015).

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Nowadays many countries present critical problems related to energy demand-supply equilibrium. Petroleum-based products has been used as energy sources since Industrial Revolution but it is well known that they are not environmental friendly and reserves of this source are unable to face future demand for more than three decades. So, the focus on alternative sources has been strongly directed to biomass. This word is used to designate several fruit oils (including castor bean oil) which present the characteristics of being sustainable sources which are also entitled with the advantage of being a labor intensive source, adequate to underdeveloped tropical regions. This paper put forward a new approach, based on the principles of Supervisory Control Theory and **Petri** **nets**, aiming the co- ordination of logistics flows in agribusiness chains, focusing the castor bean biodiesel supply chain. A framework for supervisory control in logistics systems is proposed. Most of the relevant activities in the castor bean biodiesel supply chain were surveyed to support the proposed modeling process. A mathematical model was developed using **Petri** **nets** and the control constraints of the model could be determined through computational simulation. Several scenarios could be conceived and the controlled system presented an acceptable performance. As conclusion, it seems clear that the proposed approach is a feasible and useful tool for the modeling, control and analysis of agribusiness chains.

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Reo [1] is a channel-based coordination language which has its main application area in component and service composition. The idea in Reo is to construct complex, so-called connectors out of a set of user-defined primitives, most commonly channels. Among a number of sophisticated features, such as mobility [11], context-dependency [6, 5] and dynamic reconfigurability [14], on a more basic level Reo can be seen also as a model of concurrency. Comparing Reo with **Petri** **nets**, the first obvious common- ality is the fact that they both use a graph-based model, i.e. their structure can be modeled using typed graphs. Moreover, both models combine control-flow and data-flow aspects. In this paper, we are par- ticularly interested in the concurrency properties of the two models, i.e. parallel or synchronized actions vs. interleaved or mutually excluded actions. To understand the relationship between Reo connectors and **Petri** **nets**, we follow an approach in this paper where we map both models to so-called port au- tomata [13], which serve as our common semantical domain. We can thereby gain an integrated view on structure and semantics of Reo connectors and **Petri** **nets** and moreover compare both models.

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Abstract. Nowadays many countries present critical problems related to energy demand- supply equilibrium. Petroleum-based products has been used as energy sources since Industrial Revolution but it is well known that they are not environmental friendly and reserves of this source are unable to face future demand for more than three decades. In this scene, the focus on substitutive sources has been strongly directed on biomass. This word is used to designate several fruit oils (including mamona) presenting the characteristics of being sustainable sources which also are entitled with the advantage of being a labor intensive source, adequate to underdeveloped tropical regions. This paper treats on the application of **Petri** **nets** to model the mamona biodiesel supply chain aiming to provide insights to help decision making when managing that chain. Through simulation of several operational scenarios one could show that the conceived model is very useful to guide optimized interventions on the mamona biodiesel supply chain.

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In this paper, we propose the analysis of the mega-data base which allows the classification of over than one thousand articles dealing with discrete event systems described by **Petri** **nets** and their extensions. The establishment of this database will allow future researchers to easily start their research through:

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The **petri** **nets** can be useful in determining the possible activations in the neural network and achievable conditions. The graph of **Petri** **nets** can follow all possible input examples of neural network. It can be seen where the neural network A has a correct result and where - not. Thus, by displaying the authenticity of the result in the neural network could be found ways to improving it. There is the possibility of conducting research on different architectures of neural networks. The **petri** **nets** could help to find a suitable architecture of the neural network. The results can be very useful in training of the neural networks. By imaging the neural network through graph of **Petri** **nets** could be found on the appropriate input examples with which to be trained network. So can be significantly reduced training time. Just should be selected input examples with two markers in the graph (or without markers) of the **Petri** net. Training neural networks can be much facilitated. The results can be applied in lectures and education on neural networks. The study of specific architecture of the neural network can be examined with **Petri** **nets**. Here it can be determined which is the appropriate neural network for the specific subject area and the specific problem. Thus can predict which architecture of the neural network will be most suitable (how many layers, how many neurons).

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The places Audit Table 1,2 and 3 are used to model the audit tables of three different relations in the operational sources and receive tokens representing the final audit r[r]

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Although it is not guaranteed yet that the target marking would be found with our heuristically guided partial exploration algorithm without complete exploration of the[r]

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RFID (Radio Frequency Identification) technology is being used increasingly on industrial and logistics aplications, however, just as a manner of enabling item identification. In this work, a model based on **Petri** **Nets**, proposed by [2] is implemented, that, besides the identification of the product, it allows to update the item state in relation to the expected process in real-time. The **Petri** Net in question was named PNRD (**Petri** Net Inside RFID Database) and defines that RFID tags are used as a database containing the item identification, the expected process that said item will go through (stored on the Incident Matrix from the PNRD) and the current state of the item, besides that, in the middleware, are the information about how the process advances in function of pre- conditions determined from reads from the tags (antenna, distance, state of tag) needed to trigger the **Petri** Net’s transition. This work presents the implemented middleware to extract information from tags and store the trigger information from transitions. As well an example of implementation that shows a unidirectional control of a vehicle using PNRD.

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