P-graph framework provides effective algorithms to synthesize processing systems from the set of available building blocks for producing desired products. In the current work, these algorithms have been adapted for synthesizing Petri nets. Introduction Petri nets are a modeling language, that has wide range of area for description and handling concurrent, asynchronous, non-deterministic or distributed systems. Nowadays large numbers of Petri net softwares supply several built-in features both for simulation and analysis of different systems. At the same time predefined models are needed for these investigations, as Petri nets basically do not support the construction of the model. The synthesis problem for Petri nets consists in building a Petri net satisfying a given behavioral specification. Recently there are studies dealing with the synthesis based on state transition graphs [3], [2], however these works are restricted to the subclass of the bounded choice-free Petri nets. The synthesis, in general, is the act of determining the structure, network or flowsheet of a process, that performs as required. For algorithmic solution of process synthesis problems, a mathematically rigorous framework called Pgraph was introduced by Friedler et al. [5]. The method based on the wellestablished combinatorial mathematics of graph theory, and a set of axioms has been formulated to express the necessary combinatorial properties to which a feasible process structure should conform [4]. P-graphs and Petri nets have similar structures based on rigorous formal mathematical definitions and graphical notations, however the two frameworks aim at different objectives of systems design. While Petri nets are introduced primarily for modeling and analysis, P-graph framework has been developed for process synthesis. Even though the objectives are quite different, it is possible to merge their capabilities in solving specific problems, e.g., synthesizing Petri nets by the P-graph framework. Petri net synthesis by the P-graph framework The P-graph algorithms provide all of the feasible process structures. The problem is formulated by defining the set of materials and candidate operating units, characterized by their
PNSE’18 – Petri Nets and Software Engineering in2put andRoozua´tlipauLtamknaetr,erFiearlesn,caFsriwedellelr,aBsotthoendflBowerto´raktes of their inlet and outlet streams. The materials and the operating units in P-graph correspond to the plsatcreesa mansd. Ttrhaenmsitaitoenrsiailns aPnedtrtihneeto,preersaptiencgtivuenliyt.s TinhePu-gprpaeprh bcoourrnedspoonndthteo atvhaeilabpilliatcyesoafntdhetrarnawsitimonasteinriaPlsetrainndett,hreeslpoewcetirveblyo.uTndheounppthere broeuqnudireodn tahmeoauvnatil-of deasbirielidtyporfodthuectrsawcanmabteerdiaelfisnaendd atshewelollw.eTrhbeosuenrdesotnrictthieonrseqcuoirrreedspaomnoduntot otfhe partial ndeetfi.nTithioenmofattehreiailnirtaiatelsstiantethaend the reacahraeble state in the staartce graph of Petri P-graph represented by weights of Petri net. The material rates in the P-graph are represented by arc weights in the corresponding Petri net, and the state of the P-graph is represented by in the corresponding Petri net, and the state of the P-graph is represented by tokens.
tokens.
The Solution Structure Generation algorithm of P-graph framework synthe
The Solution Structure Generation algorithm of P-graph framework synsizes all the feasible solution structures exhaustively without loss of any pothesizes all the feasible solution structure exhaustively without loss of any potentially feasible structure. The union of the feasible solution structures is a tentially feasible structure. The union of the feasible solution structures is a (maximal) solution structure itself, that is directly constructed by eliminating (maximal) solution structure itself, that directly constructs by eliminating the thmeamteartiearlisaalsndanodpeorpaetrinagtinugnitusnits
whiwchhiccahnncoatnnboetlobngelotongantyo faenaysi bfeleassitbrluectsutrruecatcu-re si msimplpeleexeaxmamplpeleininFFigiguurree11ggeenneerraatteedd bbyy PP--ggrraapphh SSttuuddiioossooftfwtwaarere[5[]1.]. acccoorrddiinngg ttoo tthhee aaxxiioommss[[35].].TThheepprrooppooseseddmmetehthooddhhasasbbeeenenddememonosntsrtartaetdedbybya a
FiguFrieg1. :1.PPetertriinneett ssyynntthheessisisbbyyP-Pg-rgarpahpahlgaolrgitohrmitshms a)aP) rPorbolbemlemb)b)MMaxaixmimaallstsrtuuccttuurree cc)) AA ffeeaassibiblelestsrtuructcuturered)d)PePtertirni entet RRefeefreernencecess 4. Friedler, F., TarCjahne,mK.l., Huan1g6, ,Y3.1W3–.3,2F0an(1,9L9.2T).: Combinatorial Algorithms for synthesis. Comp. Eng.