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A new version of classic algorithms based on the Gauss-Jordan method were included in GHENeSys and used tocalculate a generator for the family of invariants [40]. Thus,it is possible to obtain any specific invariant as a linearcombination of vectors in the generator set.

To illustrate the method, we calculate some invariants fromthe generator, shown in Figure 13 and Figures 14. Theseinvariants are associated with plant and controller, respectively.This set of invariants matchs equations defined in Table III andTable V. Thus, it means that the system with the dynamicdescribed by the Petri net meets the desired requirements,completing the verification process.

Basic invariants calculated with GHENeSys (the first defi-nition obtainded from the generator) are shown in Figure 13.

The invariants places we want to verify are painted orangein the Figure 13 and Figure 14.

Fig. 13. Petri net invariants corresponding to the Plant

VIII. CONCLUSIONS AND FURTHER WORK

In conclusion, we can say that a design method for auto-mated systems based on UML and Petri nets that fits a model-based approach is feasible and could provide good results. Thesemi-formal characteristic of UML is a good match to earlyrequirements, while Petri Nets captures UML requirementsand can be used as its execution mode, supporting formalverification. Property analysis based on invariants can captureOCL early restrictions and stands as desired properties of thesystem, verified later, against similar properties extracted fromPetri nets associated with the final requirement model. If amatching does not occur, it is probably the case to review therequirement modeling. In such cases, UML diagrams and PetriNets already developed could serve as preliminary versions toguide the review.

In any case, the proposed method is a systematic approachfor a stepwise generation of formal specifications. It is alsoscalable when applied to large projects such as a logisticsystem to an offshore facility to explore petroleum (an ongoingproject). Therefore, the proposed method is auspicious andcan lead to a consistent way to design (discrete) automatedsystems.

Fig. 14. Invariants of Petri net corresponding to the Controller

Although UML is currently broadly used for requirementsspecifications, we avoided the inclusion of direct functionalrepresentations, such as use-cases, criticized by several authors[41]. Petri Nets conversion would be quite evident from use-case diagrams. On the other hand, it also brings the possibilityof missing non-functional requirements, which can destroycompleteness - some times consistency - of requirement mod-els. Therefore, the use of goal-oriented methods [42] - wherefunctional and non-functional requirements collapse into thesame goal - emerges as a good alternative, especially to thedesign of automated system.

Thus, as further work, we intend to substitute the repre-sentation of elicited requirements, from UML to goal-orienteddiagrams - such as KAOS [43]. The performance of the newapproach will be compared with traditional projects alreadymade in UML. Another promising feature is to enhancePetri Nets modeling by introducing High-Level Petri Nets(HLPN) or Hierarchical Hith Level Nets (HHLPN). That willalso require the development of new algorithms to calculateinvariants in folded nets and algorithms to transfer KAOSdiagrams to Petri Nets [15].

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Arianna Z. Olivera received a bachelor in Com-puter Scince from the Universidade de Oriente, San-tiago, Cuba, and is finishing her PhD in Mechatron-ics Engineering at the Universidade de São Paulo,Brazil. Her research interests are in modeling andanalysis and simulation of processes using PetriNets. She is up to become a faculty staff at FederalUniversity of Pernambuco.

Pedro M. G. del Foyo received the B.E. degree inautomatic control from “Julio A. Mella” PolytechnicInstitute, Santiago, Cuba, in 1992 and a M.S. degreein 2001 and PhD degree in 2009 in MechatronicsEngineering from University of São Paulo, Brazil.Presently he is a professor at the Federal Universityof Pernambuco, Dept of Mechanical Engineering.His current research interests include the design,analysis and verification of complex systems, withfocuses on distributed, embedded and real-time sys-tems and scheduling algorithms based on state space

analysis techniques.

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José R. Silva received the B.S. in Physics a M.S. inAtomic Physics from Federal Universities of Bahiaand Pernambuco in Brazil, a M.A. in Interdisci-plinary Computer Science by Mills College, CA,USA, and a PhD in Computer Engineering in 1992by the University of São Paulo, Brazil. Had post-doctoral positions in Computer Science and SystemsDesign at the University of Waterloo, Canada. Hismain interest is in formal methods for EngineeringDesign based on Petri Nets, Knowledge Engineeringfor Planning and Scheduling and Intelligent Manu-

facturing Processes. Presently he is a senior associate professor at Universityof São Paulo, Dept. of Mechatronics Engineering.