Defining and Implementing Dynamic Semantics of Object Oriented High Level Petri Nets

Transcription

1 Defining and Imlementing Dynamic Semantics of Object Oiented High Level Peti Nets Maius Bezovan Faculty of Automation Comutes and Electonics, Univesity of Caiova 1100 Caiova, Romania Abstact. This ae deals with the dynamic semantics of a new oosed fomalism, called Object Oiented High Level Peti Nets (OOHLPN). In the fist at of the ae, the fomal definition of OOHLPN is biefly intoduced, and an examle of using OOHLPN is ovided. The second at of the ae esents the dynamic semantics of OOHLPN. Fist, the semantics of Extended High Level Peti Nets with Objects (EHLPNO) is descibed. These nets ae based on standad of High Level Peti Nets, eniched with some object-oiented concets. Next, the semantics of OOHLPN is descibed using notions of state, making, ste and ste fiing. The thid at of the ae esents some algoithms fo imlementing the dynamic semantics of OOHLPN. 1 Intoduction Peti nets ae gahical and mathematical tools used in diffeent aeas whee the notion of events and concuence aea. To secify lage systems, many high level Peti nets fomalisms has been develoed, such as Pedicate/Tansition Nets [9], Coloed Peti Nets [10] and Algebaic Nets [12]. Duing the last yeas, thee have been many oosal of intoducing object-oiented featues into the fame of Peti nets to incease the owe fo modeling concuent and distibuted systems: PROT nets [1], POTs and POPs nets [11], OBJSA nets [4], CO-OPN [8], Cooeative Nets [2, 3], LOOPN language [11], Pntalk language [7]. In this ae a new oosed fomalism called Object Oiented High Level Peti Nets (OOHLPN) is esented, which is based on the standad of High Level Peti Nets. These nets ae constucted using two elements: (a) to allow tokens fom a Peti net to be instances of some classes, and (b) to tansfom a Peti net into a class, allowing its instances to exist inside anothe Peti nets. To define OOHLPN, fist Extended High Level Peti Nets with Objects (EHLPNO) ae defined, and also the classes associated to EHLPNO. The second at of the ae descibes the dynamic semantics of OOHLPN in two stes: fist the semantics of EHLPNO is esented, and next the semantics of the entie OOHLPN is descibed. The thid at of the ae esents some methods and algoithms fo imlementing the dynamic semantics of OOHLPN.

2 551 2 The Fomal Definition of Object Oiented High Level Peti Nets The definition of Object Oiented High Level Peti Nets is made in two stes: (a) by modifying High Level Peti Nets, allowing tokens to have objects as values [6], and (b) by tansfoming a High Level Peti Net into a class, allowing Peti nets to exist inside othe objects. In the fist ste, a class of nets called Extended High Level Peti Net with Objects (EHLPNO) is defined, which eesent High Level Peti Nets eniched with some object oientation concets such as: (a) ceating new objects inside tansitions, when they fie, and (b) calling ublic methods of objects inside tansitions. Objects can exist inside Peti nets as token assigned to some vaiables. To ceate an object inside a tansition, a syntactical constuction called object ceation secification is used, which is defined as: x.ceate(<aams>) whee <aams> is a list of exessions of tems comatible with the fomal aguments of the method ceate of the class associated to x. The set of all object ceation secifications is denoted by CREATE. In tems of Peti nets, a method can be viewed as a subnet of an enclosing net, having an inut lace containing the inut tokens of the method, and an outut lace fo the esulting tokens. Tansitions contained in the subnet eesent the actions efomed by that method. The subnet associated to a method is not necessay to be exlicit secified; only its inut and outut laces. A method is defined as a tilet of the fom (m, #m, m#), whee m eesents the name of the method, #m its associated inut lace, and m# the associated outut lace. The lace #m is also an inut lace of the enclosing net, and m# is also an outut lace of the enclosing net. At most one of the elements #m and m# can be the emty symbol λ, in the case when thee aen t inut o outut tokens fo that call. The set of all methods is denoted by METH. Thee ae consideed two tyes of method call. Let t be a tansition and x a vaiable associated to t, which is bound to an object ob. A method call is a syntactical constuction having one of the following foms: x.m(a), which eesent an asynchonous call, b x.m(a), which eesent a synchonous call, whee: m is a ublic method fom the class associated to the object ob; a is an exession containing outut vaiables of t; when evaluated, it esults a multiset of tokens ove the inut lace #m; b is an exession containing inut vaiables fo t; when evaluated, it esults a multiset of tokens ove the outut lace m#. In the following, MC will denote the set of all method calls. The semantics is defined fo each tye of method call. Let t be a tansition containing a call of a method m of an object bound to a vaiable x associated to an ac incident to t. 1. Fo an asynchonous call the calling tansition t is extended with an exta outut ac connected to the inut lace of the called method m, as is esented in Figue 1.

3 Fo a synchonous call the calling tansition t is extended with a subnet containing a stat tansition t#stat, an end tansition t#end and a waiting lace t#wait. The stat tansition is connected with the inut lace of the called method m, and the end tansition is connected with the outut lace of m, as is esented in Figue 2. t t a x a a t#stat #m t Fig. 1. Asynchonous call t t a x a a t#stat t#end b t t#wait #m m# b Fig. 2. Synchonous call b Data tyes contained into a class ae managed though algebaical secifications [8]. To allow intoducing the notion of inheitance, well-stuctued hieachical algebaical secifications [5] will be used instead of algebaical secifications. Definition 1. Let S=(S, O, V, EQ) be a well-stuctued hieachical algebaical secification. An Extended High Level Peti Net with Objects is a tule: Ehlno = (NG, Sig, V, H, Tye, AN, M 0, ON, Y), whee: Hln = (NG, Sig, V, H, Tye, AN, M 0 ) is a standad High Level Peti Net; ON = (TCeate, TCall) is the object net annotation: TCeate:T (CREATE), is a function which assign object ceation secifications to tansitions; TCall:T MC {λ}, is a function assigning at most one method call to each tansition; Y is a set of S-indexed vaiables, disjoint fom V, eesenting the set of initialization aametes. When use an instance of an EHLPNO, the vaiables fom the initialization set must be elaced by the actual values.

4 553 Let Ehlno be an EHLPNO and σ an assignment fo vaiables fom Y, σ σ Y. An instance of Ehlno is denoted by (Ehlno, σ) and it is a standad High Level Peti Net obtained fom Ehlno by efoming the following actions: the substitution of all tansitions having method calls with thei coesonding subnets, accoding to figues 1 and 2, the substitution of all occuences of vaiables fom Y with thei bindings. The set of all instances of Ehlno is denoted by EInst(Ehlno). An EHLPNO can be tansfomed into a class. In the following, SORT will denote the set of all sots, and SORT Cl will denote the set of the tyes of all classes, SORT Cl SORT. Definition 2. Let Ehlno be an EHLPNO. A class associated with Ehlno is a tilet: Cl = (S, I, Ehlno). whee: S = (S, O, V, EQ) is the hieachical algebaical secification associated with Ehlno; I = (s, s I, M) eesents the inteface of the class, whee: s SORT Cl eesents the sot of the class; s I is a atial ode elation on the set SORT Cl, secifying the ascendancies of the cuent class s; M METH, eesents the ublic methods of Ehlno; The set of all classes associated with EHLPNO will be denoted with CLASS. An instance of a class associated with an EHLPNO is defined in tems of algebaical secifications. Fo an algebaical secification S = (S,O,V,EQ), an instance of S is a ai (S, σ), whee σ σ V. The instance set of the secification S is denoted by SInst(S). Let Cl = (S, I, Ehlno) be a class associated to Ehlno = (NG, Sig, V, H, Tye, AN, M 0, ON, Y). An instance of the class Cl is an object ob defined as follows: ob = ((S,σ), I, (Ehlno,σ 1 ))), whee: σ σ V, σ 1 σ Y, (S,σ) SInst(S), (Ehlno,σ 1 ) EInst(Ehlno). When using objects inside a Peti net, a vaiable is not bound to an object, but to a efeence of the object. This efeence can be etained by a ma, denoted ef, which associates to each object an object identifie. In the following OID will denote the set of all object identifies, and OB will denote the set of all objects. The ma ef is a bijective function defined as: ef: OID OB, ef(oid) = ob = ((S, σ), I, (Ehlno, σ 1 )), whee σ σ V, σ 1 σ Y. The notion of inheitance is defined on the set SORT Cl as an ode elation. Let s 1,s 2 SORT Cl be two tyes of classes associated with two EHLPNOs Ehlno 1 and Ehlno 2 and let Cl 1 = (S 1, (s 1, I s1, M 1 ), Ehlno 1 ), Cl 2 = (S 2, (s 2, I s2, M 2 ), Ehlno 2 ) be thei associated classes. The class of tye s 2 inheits the class of tye s 1 and it is denoted Cl 1 I Cl 2 iff: (s 1, s 2 ) I s1 M 1 M 2

5 554 S 1 H S 2 Ehlno 1 Sem Ehlno 2 The elation H is defined ove well-stuctued hieachical algebaical secification. S 1 H S 2 iff S 2 is obtained fom S 1 by using zeo o moe oeatos and +. The elation Sem concens the semantics of the associated nets. Ehlno 1 Sem Ehlno 2 iff thei eachability gahs ae (stongly) bisimila in the sense of Milne and Pak. Let SP = {S 1,, S n } be a set of well-stuctued hieachical algebaical secifications. A class hieachy associated to SP is a set of classes togethe with the inheitance elation: H = {Cl k = (S k, I k, Elno k ) S k SP} A oot of the hieachy H is a class Cl = (S, (s, s I, M), Ehlno) fo which s = Φ. Definition 3. Let SP = {S 1,, S n } be a set of well-stuctued hieachical algebaical secifications. An Object Oiented High Level Peti Net associated to SP is a class hieachy with a single oot: Oohln = {Cl 0, Cl 1,.., Cl n }, whee, fo k=1, n, Cl k = (S k, I k, Elno k ), S k SP, so that Cl 0 is the main oot of Oohln. The main oot of an OOHLPN is imotant when defining the dynamic semantics of these nets. It eesents the highe level of abstaction fo a modeled system, and an instance of Cl 0 it is the unique object, which exists at the beginning of the dynamic system evolution. In the following it is esented an examle of using OOHLPN fo modeling a flexible manufactuing cell. The manufactuing cell has six comonents, as esented in Figue 3: an inut buffe IN, which eceives the ieces to be manufactued, and an outut buffe OUT whee the manufactued ieces ae stoed; two manufactuing machines, M 1 and M 2 ; an obot R, used to load and unload the machines; an intenal buffe B, used to stoe the unfinished ieces. The ieces ae suosed to equie two odeed oeations, o 1 and o 2, each oeation on a single machine: o 1 on machine M 1 and o 2 on M 2. IN R OUT M 1 M 2 Fig. 3. A simle manufactuing cell To descibe the functionality of the manufactuing cell, the following classes ae used: the class Robot, which descibes the functionality of the obot R; B

6 555 the class Machine, which descibes the functionality of the machines M 1 and M 2 ; the class Cell, which descibes the functionality of the entie manufactuing cell. The OOHLPN fo the manufactuing cell is: Oohln = {Cell, Machine, Robot} whee Cell is the main oot class of the hieachy, each class being hieachical indeendent. The EHLPN of the class Robot is esented in the Figue 4. It has a single ublic method, (move, #move, move#), which is used when the obot must move a iece fom a souce lace to a destination lace. All laces have a single stuctued tye fo tokens with thee comonents, (x, y, z), eesenting 3D coodinates, and the lace InitPos is the only lace with a non-emty making. The EHLPN of the class Machine is esented in the Figue 5. It has a single ublic method, (oe, #oe, oe#), which is used when an oeation on the machine has to be efomed. Fo unifomity, all laces have stuctued tokens as in the class Robot, and the lace Available is the only lace with a non-emty making. To descibe the EHLPNO associated with the class Cell, a ule-based like language is used. Each tansition is descibed by a ule, whee the antecedent and the consequent eesent some laces of the net. The following six ules descibes the functionality of the manufactuing cell (the fist action of each ule consequent eesents a method call): Available t 1 Fixing Oeating Defixing t 2 t 3 t 4 #oe oe# Fig. 4. The Extended High Level Peti Net associated with the class Machine InitPos t 6 ToInitPos ToSouce Picked ToDest Doed t 1 t 2 t 3 t 4 t 5 #move move# Fig. 5. The Extended High Level Peti Net associated with the class Robot

7 556 t 1 : if (iece available on IN) (R available) (M 1 available) then (R : move In M 1 ) (R available) (M 1 loaded) end t 2 : if (M 1 loaded) then (M 1 : oeation) (iece available on M 1 ) end t 3 : if (iece available on M 1 ) (R available) then (R : move M 1 B) (R available) (iece available on B) end t 4 : if (iece available on B) (R available) (M 2 available) then (R : move B M 2 ) (R available) (M 2 loaded) end t 5 : if (M 2 loaded) then (M 2 : oeation) (iece available on M 2 ) end t 6 : if (iece available on M 2 ) (R available) then (R : move M 2 OUT) (R available) (iece available on OUT) end M 1 #IN OUT# t 1 m 1 m 1 M 1 L M 1 O M 2 O M 1 I m 2 t 5 t2 R M 2 I m 2 M 2 L t 3 t 4 M 2 Fig. 6. The Extended High Level Peti Net associated with the class Robot The EHLPNO associated with Cell is esented in Figue 6. The lace R contains instances of the class Robot as tokens, while the laces M 1 and M 2 contain instances of the class Machine. The laces #IN, OUT#, B, M 1 I, M 1 L, M 1 O, M 2 I, M 2 L, M 2 O have stuctued tokens with eight comonents, each comonent being a 3D oint coesonding to the eight laces whee the obot can move (the inut an the outut lace of the machine M 1, the inut an the outut lace of the machine M 2, the inut an the outut lace of the buffe B, the inut lace of the buffe IN and the outut lace of the buffe OUT) denoted by {m 1 i, m 1 o, m 2 i, m 2 o, bi, bo, in, out}. The laces with non-emty initial making ae M 1, M 2, R, M 1 and M 2 I.

8 557 The method calls associated with the tansitions ae the followings: t 1 :.m 1 i.move(.in) t 4 :.m 2 i.move(.bo) t 2 :.m 1 o m 1.oe(.m 1 i) t 5 :.m 2 o m 2.oe(.m 2 i) t 3 :.bi.move(.m 1 o) t 6 :.out.move(.m 2 o) The class Cell has two ublic methods, (IN, #IN, λ) and (OUT, λ, OUT#), used to ut a iece into the cell, o to extact a finished iece fom the cell. 3 Defining Dynamic Semantics of Object Oiented High Level Peti Nets An OOHLPN descibes a class of systems with simila oeties. To model a aticula system, some instances of the classes contained into the OOHLPN hieachy have to be ceated, and next thei concuent activities have to be handled. Let S SORT Cl be a set of class tyes. The set of all object identifies fo the classes associated to S, Cl(S) = {((S, O, V, EQ), I, Ehlno) s S}, can be stuctued like a Sig-algeba, called identifies algeba, ove which a atial ode elation induced by the ode elation I is ovelaed. Fo S, the atial ode elation of classes is detemined as follows: S I = s S ( s I ). Now, the infomal constuction of the family of sets (OID s ) s S is the following: OID s = {oid(s, k) k= 1, 2,... }, whee k is the ode numbe of the cuent object. So, the fist ceated object fom the class (S, (s, s I, M), Ehlno) Cl(S) class will have the efeence (s,0), the second (s,1), etc. In the following, the dynamic semantics of OOHLPN will be defined in two stes: (a) fo an instance of a class associated to an EHLPNO, and (b) fo the entie set of instances eesenting an OOHLPN. Fo handling the dynamic evolution of the objects fom an OOHLPN, the notion of dynamic link will is used. Let Oohln={Cl 1,,Cl n } be an OOHLPN. A dynamic link is a ai (oid, ef(oid)), fo which thee exists a class Cl = ((S,O,V,EQ), I, Ehln) Oohln, and a sot s S, such that: oid OID s. To ceate an object ob of a class, an object identifie oid have to be ceated, and a efeence to that object, ef(oid) = ob, so that (oid, ef(oid)) eesents a dynamic link fo the object ob. The cuent state of an object is done by the cuent making of its associated EHLPNO. Definition 4. Let Ehlno be an EHLPN, Cl=(S, I, Ehln) be a class associated with Ehlno, and ob=((s,σ), I, (Ehlno,σ 1 ))) be an object of Cl with a dynamic link (oid, ef(oid)). The cuent state of ob is a ai (oid, M), whee M is the cuent making of the instance (Ehlno,σ 1 ) EInst(Ehlno).

9 558 The notion of occuence mode of a tansition can be defined. The occuence mode secifies the bindings fo the vaiables associated to a tansition. Denoting by t a tansition, the following notations will be used: VaIn(t), eesenting the set of vaiables attached to inut acs of t, VaOut(t), eesenting the set of vaiables attached to outut acs of t, Va(t) = VaIn(t) VaOut(t), eesenting the set of all vaiables attached to t. Definition 5. Let Ehlno be an EHLPN, Ei = (Ehlno, σ 1 ) EInst(Ehlno) one of its instances and t be a tansition of Ei. An assignment α of the set of vaiables Va(t) is called occuence mode fo t if thee exists an evaluation Val α in TERM(O V) so that the following statements hold: if TCeate(t) Φ, then x VaOut(t)-VaIn(t), α(x)=x.ceate(a 1,...,a n ), so that ef(oid)=ob, whee x.ceate(a 1,...,a n ) TCeate(t); the selecto TCond(t) can be evaluated; all multisets associated to incident acs of t can be evaluated. To define the enabling condition fo a tansition, the multiset of tems associated with an ac can be extended by using a ma denoted ac: ac: (P T) (T P) TERM(O V) Φ, ac(u, v)=a(u, v), if (u, v) F, ac(u, v)=φ, if (u, v) F A tansition t is enabled in a making M fo a aticula assignment fo its vaiables if thee ae enough tokens into the inut laces of the tansition. Definition 6. Let ob=((s,σ), I, (Ehlno,σ 1 ))) be an object with a dynamic link (oid,ef(oid)), (oid,m) be its cuent state, t be a tansition in the instance (Ehlno,σ 1 ) and α be an occuence mode of t. The tansition t is enabled with the occuence α in the state (oid,m) and is denoted (oid,m)[t:α, iff the following condition is satisfied: P, Val α (ac(, t)) M() An enabled tansition t may fie. Definition 7. Let ob=((s,σ), I, (Ehlno,σ 1 ))) be an object with (oid, ef(oid)) a dynamic link, (oid, M) be its cuent state, and t an enabled tansition in the instance (Ehlno, σ 1 ). The fiing of t leads ob to the next state (oid, M 1 ), which is denoted by (oid, M)[t:α (oid, M 1 ), and defined as follows: P, M 1 () = M() - Val α (ac(, t)) + Val α (ac(t, )) Remak. When a tansition t contained into an object ob fies, this cause the changing of the cuent state of ob, and also the changing of the state of othe objects having ublic methods, if these methods ae called inside of t: If t is a stat tansition and #m is the inut lace of the called method m, contained into an object: ob 1 = ef(oid 1 ) = ((S 1, σ), I 1, (Ehlno 1, σ 1 ), having a dynamic link (oid 1, ef(oid 1 ), and the state (oid 1, M 1 ), then its new following state will be: (oid 1, M 1 )[t:α (oid 1, M 1 1 ) whee:

10 559 M 1 1 (#m) = M 1 (#m) + Val α (ac(t, #m)) If t is an end tansition and m# is the outut lace of the called method m, contained into an object: ob 1 = ef(oid 1 ) = ((S 1, σ), I 1, (Ehlno 1, σ 1 ), having a dynamic link (oid 1, ef(oid 1 ), and the state (oid 1, M 1 ), then its new following state will be (oid 1, M 1 )[t:α (oid 1, M 1 1 ), whee: M 1 1 (#m) = M 1 (#m) - Val α (ac(m#, t)) Now, the dynamic semantics of an entie OOHLPN can be descibed. The state of a modeled system is eesented by the states of all cuent objects secified by thei dynamic links. At the beginning of the system evolution, thee is a unique object, which is instance of the oot of the OOHLPN. Definition 8. Let Oohln be an OOHLPN. (1) The initial state of Oohln is the unique dynamic link associated to the oot of Oohln: SA 0 = {(oid 0, ef(oid 0 )) oid 0 OID 0 } (2) A state of Oohln is a finite set of dynamic links: SA = {(oid, ef(oid)) Cl=((S,O,V,EQ),I,Ehln) Oohln, s S : oid OID s } Each object fom the cuent state of an OOHLPN has an associated EHLPNO with a cuent making. All these makings eesent the cuent making of the OOHLPN. Definition 9. Let Oohln be an OOHLPN. (1) A making of Oohln coesonding to a state SA of Oohln is the set of all object states: OM = {(oid, M) (oid, ef(oid)) SA} (2) The initial making of Oohln in the initial state SA 0 is the state associated to the object oid 0 : OM 0 = {(oid 0, M 0 ) (oid 0, ef(oid0)) SA 0 } The making of an OOHLPN is changing evey time when the state of an object fom the cuent state of the net is changed. Definition 10. Let SA be a state of an OOHLPN Oohln, and OM be its making in the state SA. (1) A ste Y is a set of enabled tansitions contained into objects of the state SA, each object fom SA having exactly one enabled tansition in Y. (2) The ste Y fies and leads Oohln to a new state SA 1 and a new making OM 1 unde this state, iff all tansition fom Y fie. The new state is : SA 1 = SA - Destoy(Y) Ceate(Y), whee: Destoy(Y) eesents the set of all objects destoyed in the cuent state SA, and Ceate(Y) eesents the set of all objects ceated in the cuent state SA: Destoy(Y) = t Y {(σ(x), ef(σ(x))) x VaIn(t) - VaOut(t)} Ceate(Y) = t Y {(σ(x), ef(σ(x))) x.ceate(a 1,..., a n ) C(t)}; The new making is: OM 1 = {(oid 1, M 1 ) (oid 1, ef(oid 1 )) SA 1 } whee:

11 560 if (oid 1, ef(oid 1 )) SA and (oid 1, M) M, then t Y with occuence α and (oid 1,M)[t:α (oid 1, M 1 ), if (oid 1, ef(oid 1 )) SA, then: (oid 1, M 1 ) = (oid 1, M 0 ). Passing to a new state with a new making is denoted: SA[Y SA 1, OM[Y OM 1. 4 Imlementing Dynamic Semantics of Object Oiented High Level Peti Nets The imlementation of the dynamic semantics of OOHLPN is made in two stes: in the fist ste the semantics of EHLPNO is imlemented and next the semantics of the entie OOHLPN. An otimized vesion of token-laye algoithm is used fo imlementation, which is based on launch laces [13]: each tansition has an associated launch lace, chosen fom the set of its inut laces. If this lace has an emty making then doubtlessly the tansition isn t enabled, else the tansition is ossible to be enabled. An Extended High Level Peti Nets with Objects Ehlno eesents the body of a class Cl. Fom a ogamming language view, all classes associated with EHLPNO ae deived fom a distinct base class, called CPNO. The algoithms which imlement the dynamic semantics of EHLPNO ae membe functions of CPNO. The constucto of CPNO exands in the initial net each tansition having method calls with its associated subnets, efom the initial making of the net, constucts the list -enabled of ossible enabled tansitions and next it call the TokenPlaye ocedue which descibes the dynamic evolution of the net. ocedue CPNO::Ceate(Y) NetExanding() InitMaking(Y) InitEnabled() TokenPlaye() end The TokenPlaye algoithm can be descibed as follows: ocedue CPNO::TokenPlaye() enabled-list GetEnabledTansitions() while enabled-list Φ do t SelectEnabledTansition(enabled-list) FiingTansition(t) enabled-list GetEnabledTansitions() od end The function SelectEnabledTansition chose an enabled tansition fom the set of all cuent enabled tansitions of the net, and it eesents non-deteminism in the dynamic evolution of the net. The function GetEnabledTansitions detemines all enabled tansitions, based on the function Enabled:

12 561 logical function CPNO::Enabled(t) fo * t do if (Match(Eval(A(,t)),M()) then etun false fi od if Tye(t)=end-call then tok GetObject(TCall(t)). OututMethodPlace(GetMethod(TCall(t))) if Match(Eval(OututVaiables(TCall(t))),tok) then etun false fi fi if Eval(TC(t)) then etun false fi etun tue end The function Eval evaluates a multiset of vaiables accoding to thei bindings, and the function Match efoms a matching action between a multiset of vaiables and a multiset of constants, and, if ossible, efoms the binding oeation fo vaiables. Fo a ublic method (m, #m, m#) defined in the inteface I of the class Cl, the functions OututMethodPlace and InutMethodPlace etun the cuent making of the laces m# and #m esectively. The ocedue FiingTansition efoms the fiing oeation and udates the list -enabled unde the new making. ocedue CPNO::FiingTansition(t) fo * x VaIn(t)-VaOut(t) do DeleteOject(x) od fo * t do DelTokens(M(), Eval(A(,t))) DelEnabled() od if Tye(t)=end-call then tok GetObject(TCall(t)). OututMethodPlace(GetMethod(TCall(t))) GetObject(TCall(t)). DelTokens(tok,Eval(OututVaiables(TCall(t))) fi fo * c TCeate(t) do CeateOject(Vaiable(c),Paams(c)) od fo * t do

13 562 AddTokens(M(), Eval(A(t,))) AddEnabled() od if Tye(t)=stat-call then tok GetObject(TCall(t)). InutMethodPlace(GetMethod(TCall(t))) GetObject(TCall(t)). AddTokens(tok,Eval(InutVaiables(TCall(t))) fi end The functions AddEnabled and DelEnabled udate the list -enabled. The function CeateObject calls the constucto fo a secified object and un indiectly its Token- Playe method. An OOHLPN Oohln is a class hieachy with a single oot, and the modeling of a concuent system is made by the set of cuent dynamic links, eesenting the cuent state of Oohln, and by the making of the cuent state: Oohln = {Cl 1,..., Cl n }, SA = {(oid, ef(oid) Cl=(S,O,V,EQ) Oohln, s S: oid OID s } OM = {(oid, M) (oid, ef(oid)) SA} Duing the dynamic evolution of the modeled system, the objects contained into the cuent state of the OOHLPN have a elatively indeendent evolution, the only inteactions between these objects being method calls. To imlement the dynamic evolution of an OOHLPN, the notions of state, making, ste and ste fiing have to be managed. To manage the cuent state SA of an OOHLPN, means to manage the concuent evolution of the objects contained into SA. That is a latfom deendent oblem, and thee ae thee main solutions: (a) Fo a sequential ogamming envionment, a vitual concuency can be ealized using a small kenel ogam that maintains a list of active objects and ovides imitives to add/emove objects to/fom the list. The kenel must have a schedule, which activate each object by calling its TokenPlaye function. (b) Fo an envionment which suots theads, all objects ae unning concuently on the same machine, each object in its own thead. (c) Fo a distibuted envionment, all objects ae unning in aallel, eventually on diffeent machines. Initially thee is a single object coesonding to the dynamic link (oid 0, ef(oid 0 )), which eesents the initial state SA 0. The initial making of the net associated to oid 0, and its dynamic evolution will ceate new objects and will destoy othes. Excet fo the object which is the instance of the oot class of the hieachy, all othe objects ae ceated by the function CeateObject, which is called within the functions InitMatking and FiingTansitions of an aleady ceated object. The objects can be destoyed only by the function DeleteObject, called within the function FiingTansition of an object.

14 563 When use theads, the ocedue TokenPlaye of a new ceated object ob k uns in the thead of the othe object ob j which ceates ob k. The ocedue TokenPlaye of the object ob 0 uns in the main thead. A ste is a set of enabled tansitions contained into objects of the cuent state, one enabled tansition in each object. Because the function SelectEnabledTansition selects only one enabled tansition fom the net associated to the cuent object, it esults that the set of tansitions etuned by the function SelectEnabledTansition of all cuent alive objects eesents the cuent ste. The fiing of the cuent ste is made by the call of the function FiingTansition of all cuent alive objects. In conclusion, to imlement the dynamic semantics of an OOHLPN it is necessay: to imlement the dynamic semantics of EHLPNO; to coodinate a system of concuent objects, which eesent instances of classes associated to EHLPNO. 5 Conclusions In this ae, secification fomalism fo discete event systems, called Object Oiented Peti High Level Nets is oosed. The OOHLPN fomalism has been oosed fo the need to encasulate the object-oiented methodology into the Peti net fomalism. In addition, like Pedicate/Tansition nets, OOHLPN eseve the similaity with the ule-based systems. Fo this eason, a simle ule-based language used to descibe OOHLPN can be develoed, each ule of the ule base being exessed as a tansition in the coesondent OOHLPN. Thee ae descibed algoithms fo imlementing the semantics oh EHLPNO, and methods to imlement the semantics of OOHLPNO. The manne in which the dynamic semantics of OOHLPN have been defined allows a simle way to constuct a OOHLPN simulato. The C++ language can be used fo OOHLPN imlementation. All the OOHLPN concets can be imlemented using data stuctues and methods of the standad C++ language, so that the esulted class hieachy can be otable on diffeent C++ envionments. Any class fom an OOHLPN hieachy can be associated to a C++ class deived fom the CPNO class. The OOHLPN tanslato will geneate one C++ class by geneating the constucto to that class, so that the simulato fo an OOHLPN will be geneated in a semi-comiled way. Futue wok will be caied out in thee main diections: to study thooughly the connection between ule-based systems and Object Oiented High Level Peti Nets and to develo a method of imlementing dynamic semantics of OOHLPN using an infeence engine fo ule-based systems; to detemine a High Level Peti Net which is semantic equivalent to an OOHLPN; to develo a gahical and text-based language fo OOHLPN and to build a tool suoting this language.

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