Interactions among dynamic sets of objects

J. To es Æ J. A. O ega Æ M. To o In e ac ions among dynamic se s o objec s Abs ac In his pape , we p esen an ope a o o model in e ac ions among objec s. Ou p oposal allows a a iable numbe o pa icipan objec s in an in e ac ion, and his numbe will be fixed du ing he execu ion o he model. This p o ides a e y flexible in e ac ion model based on synch onous in e ac ions among se e al objec s. Ou in e ac ion model is based on e en s and allows a mul iple-way communica ion among objec s. Conc e e alues o a communica ion a e gene a ed h ough cons ain s which a e imposed locally on each pa icipan objec . The p oposed in e ac ion (and com- munica ion) model is e y e sa ile and can be used as an abs ac specifica ion mechanism. Keywo ds Communica ion ÆE en ÆIn e ac ion cons ain s ÆObjec o ien a ion ÆSpecifica ion Æ Synch onisa ion 1 In oduc ion Objec o ien a ion is based on he defini ion o a sys em by means o en i ies (objec s) ela ed among hemsel es. The p ope ies o a sys em a e exp essed h ough mechanisms like classifica ion (which g oups objec s in o classes), associa ion, gene alisa ion, specialisa ion and agg ega ion. These mechanisms cap u e s a ic e- la ionships among objec s, bu hey do no cap u e dynamic ela ionships among hem. This ype o ea u e is exp essed by means o in e ac ions ha desc ibe he way in which se e al objec s can collabo a e in a common ac ion. In objec -o ien ed p og amming languages, hese collabo a ions a e ca ied ou by means o me hods. In objec -o ien ed specifica ion languages, a mo e abs ac concep is used: he e en . An e en desc ibes an impo an momen o he sys em ha cha ac e ises wo s a es: he p e ious s a e o he e en and he s a e a e he e en . Besides causing s a e changes, e en s a e also good a coo dina ing objec s. This happens when wo o mo e objec s coincide in he same e en . The s udy o e en s has i s o igin in p ocess specifi- ca ion languages [1–3], bu hei ideas a e pe ec ly applicable o objec -o ien ed models. Objec -o ien ed specifica ion languages usually use heclien /se e model o speci y he in e ac ions among objec s. In his pape , an al e na i e o he specifica ion o in e ac ions among objec s is p esen ed. Ou p oposal is based on an n-way communica ion mechanism. This app oach appea s in he li e a u e in diffe en o ms: endez ous mul iple-way in SR [4], n-a y endez ous in LOTOS [3], ela ionships in TROLL [5, 6] andmul i- pa y synch onous in e ac ions in IP [7], among o he s. Ne e heless, all hese p oposals con empla e a fixed numbe o objec s (p ocesses) in he in e ac ion. Ou p oposal allows a a iable numbe o pa icipan objec s in an in e ac ion and his numbe will be fixed du ing he execu ion o he model. This p o ides a e y flexible in e ac ion model, wi h synch onous in e ac ions among se e al objec s. The pape is o ganised as ollows. In Sec ion 2, he main ideas o he in e ac ion among objec s and some ypical in e ac ion ope a o s used o exp ess he con- cu en beha iou o a sys em a e discussed. Sec ion 3 explains how communica ion ea u es associa ing con- s ain s o e en s can be desc ibed. Sec ion 4 p esen s a comple e applica ion example o ou in e ac ion model. Finally, in Sec ion 5 he conclusions o his wo k a e p esen ed. 2 In e ac ions A sys em can be seen as a se o objec s in e ac ing wi h one ano he concu en ly. When he sys em is ela i ely J. To es (&)ÆJ. A. O ega ÆM. To o Depa men o Languages and Compu e Sys ems, Se ille Uni e si y, A da Reina Me cedes, S/N Se illa CP 41012, Spain. E-mail: [email p o ec ed] complex, he objec app oach is e y use ul because i allows mechanisms such as inhe i ance, associa ion and agg ega ion (pe mi ing a sys em o be defined a se e al le els o abs ac ion). Each objec has a local s a e, on which local con- s ain s can be imposed. In specifica ion languages, he in e ac ion among objec s is usually based on e en s. E en s also allow communica ing pa ame e s among he diffe en objec s implied. An example is he dining philosophe s’ p oblem, which is a ypical p oblem in concu en p og amming [4]. To speci y his p oblem, he classes Philosophe and Fo k will be defined. The objec s o he Philosophe class will ha e a cyclical beha iou which consis s on hinking and ea ing. Each philosophe has o ca ch he o ks placed on his le and on his igh o ea . The e en s a e akeFo k and eleaseFo k. These names al eady gi e an idea o he in en ion o each one. The co esponding class diag am (in UML no a ion [8, 9]) is shown in Fig. 1. An impo an ac o is he numbe o objec s which pa icipa e in a communica ion. The communica ion is usually 1:1, ollowing he clien -se e app oach, wi h one-way pa ame e ans e . A mo e in e es ing ap- p oach is wo-way (n-way in gene al) communica ion among objec s. In o de o model a sys em, a synch onous model is p e e ed o an asynch onous one because he execu- ion o a synch onous communica ion e en im- media ely p o ides he pa icipa ing objec s wi h he in o ma ion ha communica ion has aken place [10, 11]. This acili a es he specifica ion o he de ec- ion o deadlocks. Mo eo e , communica ion among se e al objec s is easie in a synch onous model, while an asynch onous model is mo e ocused on one- o-one communica ions [2, 3]. I he modifica ion o he objec s a e is ca ied ou in an a omic way when i pa ici- pa es in an e en , hen synch onous in e ac ions can also be used o model ansac ions. Thus, each objec in ol ed in an in e ac ion changes i s s a e in an a omic way. This is conside ed as a change o he sys em s a e in an a omic way. The e a e many ope a o s o exp essing he con- cu en beha iou o a sys em. The mos popula ones ha e been defined adi ionally o p ocess algeb a [1–3]. LOTOS, o example, which is a language qui e ich in his sense, has h ee ope a o s o exp ess he pa allelism o p ocesses: pu e in e lea ed, ull synch onisa ion and explici synch onisa ion. I A and B a e wo p ocesses, pu e in e lea ed A ||| B deno es hei independen composi ion. In o he wo ds, bo h p ocesses do no synch onise in any e en . Full synch onisa ion A || B is a new p ocess ha deno es a pa allel composi ion in which A and B mus synch onise in all hei e en s. The e o e, we ha e a ull synch onisa ion a he p ocess le el (A and B ha e o pa icipa e, as well as hei subp ocesses) and a he e en le el ( hey ha e o synch onise in all e en s). Since an en i e subsys em has o e ol e a he same ime, i some o he pa s canno e ol e his blocks he es o he subsys em. Explici synch onisa ion A |[g 1 ,...,g n ]| is a new p ocess in which A and B mus synch onise in each e en occu ing h ough he ga es (communica ion channels) g 1 ,...,g n . Then, we ha e a comple e synch onisa ion a he p ocess le el and a pa ial synch onisa ion a he e en le el ( hey do no ha e o synch onise in all e en s). This ope a o allows a mo e flexible in e ac ion among p ocesses han he ope a o ||. Howe e , he p e ious p oblem con inues o a ise. These ope a o s desc ibe he in e ac ion o se e al p ocesses (o classes) h ough a ce ain e en . A single objec o all hose o he class can only pa icipa e o each class. Speci ying hese si ua ions wi h he abo e ope a o s may equi e specifica ions a a lowe le el, which can be complex and difficul o unde s and. E en wo se, hese specifica ions can eadily lead o ce ain p oblems, such as deadlocks. Fo example, i we sol e he dining philosophe s’ p oblem wi h his kind o in e ac ion, a philosophe can only ca ch a o k a he same ime. The incon- enience o his app oach is ha , since a philosophe fi s has o ca ch a o k (ei he he le o he igh ), and la e he o he one, a deadlock may ake place ( o example, whe e all philosophe s ca ch a o k). This is usually sol ed by adding some synch onisa ion mechanism like semapho es o moni o s [4], o by adding new p ocesses o coo dina ion, which akes us o a less clea specifica ion. Fo example, in Man ˜as [14] a solu ion is p esen ed in LOTOS wi h h ee p ocesses: •use s, which ep esen s philosophe s. Each philoso- phe fi s akes he le o k and la e he igh . Then, i eleases hem in he same o de . The philosophe s’ beha iou is in e lea ed among hem. •se ice, which ep esen s o ks. Each o k can be caugh (ei he om he igh o om he le ) and la e eleased. •wa chdog, which moni o s he philosophe s’ beha- iou , and o bids picking mo e han ou le o ks simul aneously. The e o e, he e would no be dead- locks. The e a e wo disad an ages o his specifica ion: (1) a new p ocess is added o a oid deadlocks, and (2) phi- losophe s a e obliged o ake o ks in a ce ain o de (fi s he le and hen he igh ). Fig. 1 Class diag am o he philosophe s p oblem 3 Modelling in e ac ions among dynamic se s o objec s The p oposed in e ac ion ope a o ca ies ou he syn- ch onisa ion in an indi idual way o e en s. Howe e , he key diffe ence om o he app oaches is ha he numbe o objec s o a class pa icipa ing in an in e - ac ion is no limi ed. All objec s e i ying hei con- s ain s pa icipa e in an e en , allowing in e ac ions among a dynamic se o objec s. The e a e many si ua ions whe e a dynamic se o objec s mus in e ac in an a omic way: •The coach o a eam summons all his uninju ed playe s. •A p o esso calls all hose s uden s who ailed. •A bank cancels all he accoun s o one pa icula cus ome . Fo example, an easie specifica ion om he dining philosophe s’ p oblem can be made. To a oid dead- locks, he wo o ks ha co espond o a philosophe a e assigned a he same ime, in he same in e ac ion [15]. This should be eflec ed in he class diag am in Fig. 1, changing he ca dinali y o he associa ion uses om 0..2 o 0,2 (see Fig. 4). The specifica ion o his p oblem will be s udied in mo e de ail in Sec ion 4. The main ad an age o his app oach is ha he e is no need o add new p ocesses o ensu e he coo dina- ion. Specifica ions a a highe abs ac ion le el can be ob ained wi h i . In ou model, objec s e ol e when hey synch onise in e en s. In e ac ion cons ain s define he way in which objec s o se e al classes synch onise in e en s. Each objec has a local s a e, which can only be modified o he pa icipa ion in e en s. Communica ion has o happen synch onously. An e en will occu only i each objec ha has o pa icipa e in his e en ag ees on doing i . Fu he mo e, objec s mus each an ag eemen abou he alues o he pa ame e s ha will commu- nica e among hemsel es. Fo his, each one o hese objec s es ablishes hei pa icipa ion cons ain s. This allows us o model mo e complex in e ac ions han he adi ional clien /se e app oach. E en s a e desc ibed in ou model by means o communica ion channels, which ha e he same names as he e en s. All objec s o a class sha e he communica- ion channels defined in his class. A channel is defined wi h a name and he ypes o pa ame e s communica ed wi h he e en s. In sho , he defini ion o a channel is he defini ion o an e en s empla e. 3.1 Views o a channel F om he poin o iew o in e class communica ion, i can be said ha channels cons i u e he in e ace o a class. Conc e e e en s in which objec s o a class pa icipa e occu h ough channels. When a channel is defined, i is gi en a name and i s pa ame e s a e en- ume a ed. This is he mos in e es ing ision o a channel om he local poin o iew o classes. When mo e han one objec mus synch onise in an e en h ough a channel, no all o hem need o ha e he same ision o his channel, bu he e en ha occu s will be unique. This unique e en in which se e al objec s synch onise is called a global e en . Local iews o e en s in he spe- cifica ion o a class allow us o igno e he aspec s o global e en s ha a e no ele an o his class. This ac makes his class independen om he es o he sys em. Mo eo e , objec s o a class can see diffe en global e en s in he same way, and wi h he same effec s unde he same condi ions. They may hen co espond o a single local iew. The s uc u e o a global channel is ex ac ed om he diffe en iews ha classes ha e o ha e en (local iews). These local iews o channels may ha e diffe en names, and e en he numbe o pa ame e s may be diffe en in each class. All his is unified by means o in e ac ion cons ain s among classes. Thus, each class sees wha in e es s hem om a global channel. The local beha iou o objec s o he class cli will be desc ibed wi h he no a ion {p e i }cni {pos i }. This in- dica es ha objec s o he class which e i y he condi- ion p e i , e alua ed on hei cu en s a e, will pa icipa e in he e en cn i . I he e en occu s, he s a e o pa i- cipan objec s will become he one desc ibed in pos i . The no a ion ob.a will be used o e e o he a ibu e a o an objec wi h iden ifica ion ob. The no a ion ob.exp will also be used o deno e he exp ession exp e alua ed on he s a e o he objec ob. The alue o an a ibu e a e he occu ence o an e en is ep esen ed by adding a quo a ion ma k (’) o a ibu es. Fo example, in a sys em o au oma ic banking he e a e a lo o in e ac ions, such as opening an accoun , deposi ing money and wi hd awing money. As he p oblem is qui e ex ensi e, only he close accoun e en will be s udied. The simplified class diag am wi h h ee classes is shown in Fig. 2. Cus ome class ep esen s clien s o some bank. I has wo associa ions o indica e ha a clien can ha e mul iple accoun s and se e al ca ds. Accoun class ep esen s clien s’ accoun s. An accoun can ha e se e al owne s and can be accessible by di - e en ca ds. This class has an a ibu e o deno e he Fig. 2 Pa ial class diag am o he banking p oblem balance. Ca d class ep esen s clien s’ c edi ca ds. Each c edi ca d is pe sonal. I can only belong o one clien and i is associa ed wi h one accoun . The associa ion oles a e no shown in Fig. 2. Like ole names o an associa ion, he class names ha a e in he co esponding end o ha associa ion ( o ins ance, he se o associa ed c edi ca ds o an accoun a is deno ed by he ole a.ca d) will be used. The beha iou o he classes Cus ome , Accoun and Ca d o he close accoun e en is desc ibed by he ollowing ules: 1. {a [c.accoun } Cus ome (c).closeAccoun (a) {a [ /c.accoun ’} 2. {a.balance = 0} Accoun (a).close 3. {c d.accoun = a} Ca d(c d).in alida e(a) The fi s ule means ha a cus ome can close an ac- coun i he accoun is his. A e closing an accoun , i is no ound among he cus ome ’s accoun s. The second ule allows closing an accoun i i s balance is 0. Finally, he hi d ule specifies ha a c edi ca d is in alida ed ( he objec is des oyed) when he accoun passed by pa ame e s coincides wi h he associa ed accoun . 3.2 Speci ying in e ac ion cons ain s In e ac ion cons ain s a e specified as ollows: In e ac ion cons ain s cng(pa ): cl 1 (id 1 ).cn 1 (pa 1 )[ ng 1 ]=...= cl n (id n ).cn n (pa n )[ ng n ]; ... end; whe e •cl i is he name o he classes whose objec s a e going o pa icipa e in he in e ac ion; •id i is he iden ifica ion o he objec o he class cl i ha mus pa icipa e in he e en . I is only defined when a single objec o cl i is going o pa icipa e and i s iden ifica ion is known. In ano he case, i he e en occu s, all objec s ulfilling hei cons ain s will pa icipa e; •cn i is he name o he local channel in he class cl i , and pa i i s pa ame e s (one a iable o each pa ame e ); • ng i indica es he ca dinali y o numbe o objec s o he class cl i ha mus pa icipa e h ough he channel cn i . The ange no a ion min..max will be used, whe e min indica es he minimum numbe o objec s and max indica es he maximum numbe o objec s which mus pa icipa e in he in e ac ion. To indica e ha he e is no a maximum limi , max will be an as e isk (*). The no a ion num will also be used o indica e he exac numbe o objec s. When ng i is no defined, i deno es he implici ange 1..*; •cng is he name o he global channel whose pa a- me e s a e pa . These pa ame e s a e ob ained om he local iews. The g aphical no a ion o an in e ac ion among objec s o wo classes is shown in Fig. 3. In e ac ions among mo e classes a e ob ained by gene alising his case. An e en can only occu i each class pa icipa ing in he in e ac ion has he minimum numbe o objec s indica ed in he co esponding ange. In he o he case, he e en will no be able o happen. Fo example, he specifica ion o in e ac ion con- s ain s o close an accoun is as ollows: In e ac ion cons ain s close(c,a): Cus ome (c).closeAccoun (a) = Accoun (a).close = Ca d.in alida e(a); ... end; This in e ac ion specifies ha a cus ome , he accoun indica ed by he cus ome and all associa ed c edi ca ds o he accoun should in e ac . 3.3 Examples o in e ac ions Le us conside wo in e ac ing classes cl 1 and cl 2 h ough he local channels cn 1 and cn 2 . Le us conside he pa ame e s pa 1 and pa 2 o hose channels. Some kinds o basic in e ac ions ha can be specified a e as ollows: •An objec o cl 1 in e ac s wi h an objec o cl 2 .Bo h objec s ulfil hei cons ain s and hey ag ee also in he alues o he pa ame e s pa 1 pa 2 . The e a e wo possibili ies o speci y his: – Pa icipa ing objec s o each class can be anyone ulfilling hei local cons ain s and hey may be known by he o he s pa icipa ing. This case is specified as ollows: cn(pa ): cl 1 (id 1 ).cn 1 (pa 1 )=cl 2 (id 2 ).cn 2 (pa 2 ); – Pa icipa ing objec s o each class can be anyone ulfilling hei local cons ain s and hey a e un- known by he o he s pa icipa ing. This case is specified as ollows: cn(pa ): cl 1 .cn 1 (pa 1 )[1] = cl 2 .cn 2 (pa 2 )[1]; •All objec s o cl 1 ulfilling hei cons ain s in e ac wi h all objec s o cl 2 ha also ulfil hei cons ain s. This case is specified as ollows: cn(pa ): cl 1 .cn 1 (pa 1 )=cl 2 .cn 2 (pa 2 ); Fig. 3 G aphical ep esen a ion o an in e ac ion be ween wo classes He e, all objec s o cl 1 mus ha e he same alues o he pa ame e s pa 1 . All objec s o cl 2 mus also ha e he same alues o pa 2 . Fu he mo e, all objec s mus ag ee on he alues o he pa ame e s pa 1 pa 2 . •A numbe o objec s o cl 1 ulfilling hei cons ain s in e ac wi h all objec s o cl 2 ulfilling hei con- s ain s. This case is specified as ollows: cn(pa ): cl 1 (id 1 ).cn 1 (pa 1 )[ ng 1 ]= cl 2 (id 2 ).cn 2 (pa 2 ); I o cl 1 he e a e mo e eady objec s o pa icipa e han he ones defined in ng 1 , hen he maximum numbe possible o hem will be a bi a ily chosen. •Some objec s o a class in e ac wi h o he objec s o he same class. Fo example, le us conside wo channels cn a ycn b o he class cl. The ollowing in e ac ion es ablishes he communica ion be ween wo objec s o cl h ough bo h channels: cn(pa ): cl(id a ).cn a (pa a ) = cl(id b ).cn b (pa b ); He e, we a e implici ly defining wo subclasses o objec s om cl: (1) objec s ulfilling p econdi ions o cn a and (2) objec s ulfilling p econdi ions o cn b . This kind o communica ion is simila o an in e ac- ion defined be ween wo diffe en classes. •Any combina ion o p e ious cases. This can be gene alized by making i so ha he numbe o classes can o pa icipa e in an in e ac ion. Fo example, he ollowing in e ac ion: cn(a, b, c): cl 1 .cn 1 (a, b) = cl 2 .cn 2 (b)[2..4] =cl 3 (c).cn 3 (a); deno es ha one objec o he class cl 1 will pa icipa e wi h as many objec s as possible, one objec o he class cl 2 mus ha e be ween wo and ou objec s, and one objec o he class cl 3 a single objec . Fu he mo e, he global channel cn will ha e h ee pa ame e s: •a comes om he channels cn 1 and cn 3 .This pa ame e mus ake he same alue in he objec s ha pa icipa e in he co esponding classes; •b comes om he channels cn 1 and cn 2 . The same hing mus be ulfilled as in he p e ious case; and •c comes om he iden ifica ion o an objec o he class cl 3 . The flexibili y o ou ope a o is simula ed in some o he app oaches by means o he use o ansac ions o g oups o ac ions ha a e all ca ied ou all o none o which a e ca ied ou . Howe e , ansac ions, s ill being a qui e po en mechanism, a e clea ly o a lowe le el. Fo example, i is necessa y o de ail in e media e s a es composing he ansac ion, o he o de in which i is necessa y o ca y ou each ac ion. In he p oposed in- e ac ion ope a o only he diffe en elemen s ha in- e ene in an in e ac ion a e indica ed, wi hou gi ing he conc e e de ails o how he ansac ion i sel is ca ied ou . This belongs o a la e efinemen p ocess, which will be ob ained s a ing om defined in e ac ions [16]. 3.4 Global beha iou o a sys em In o de o define he global beha iou o a sys em, i has o be conside ed wha condi ion mus be e ified so ha a global e en can occu and wha effec s his will ha e on he objec s pa icipa ing in his e en . Le us suppose ha we ha e defined he ollowing in e ac ion: cng(pa ): cl 1 .cn 1 (pa 1 )[ ng 1 ]=...=cl n .cn n (pa n )[ ng n ]; whe e he classes cl i can pa icipa e wi h he local iews cn i ,Vi[{1..n}. We will deno e cl i he popula ion o ex ension o he class cl i ,andcl i .cn i he objec s o he class cl i ha pa icipa e in an in e ac ion h ough he channel cn i . This se is composed by all objec s e i ying hei p econdi ions: Vob [cli .ob.p ei )ob [cl i .cn i I he size o cl i .cn i is g ea e han he numbe o objec s allowed o pa icipa e, hen he maximum numbe pos- sible o objec s will be (a bi a ily) chosen. The global beha iou o he sys em wi h ega d o e en cng is he ollowing: {p e}cng {pos } whe e p e : ^ (i[{1..n}) ((Vob [cl i .cn i .ob.p e i )^ (#cl i .cn i }[{ ng i })) pos : ^ (i[{1..n}) (Vob [cl i .cn i .ob.pos i ) The e o e, o allow he occu ence o a global e en , i mus be ulfilled ha each objec pa icipa ing e ifies i s cons ain s o each local iew. I mus also ha e he numbe o objec s equi ed o pa icipa e. On he o he hand, i he e en occu s, all pa icipan objec s in his e en will modi y hei s a e (in a omic way) acco ding o he local defini ion o he co esponding class. Fo example, le us conside he au oma ic banking sys em shown p e iously in Sec ion 3.1 wi h he ol- lowing h ee ules 1. {a [c.accoun } Cus ome (c).closeAccoun (a) {a [ /c.accoun ’} 2. {a.balance = 0} Accoun (a).close 3. {c d.accoun = a} Ca d(c d).in alida e(a) and he ollowing in e ac ion o close an accoun : close(c,a): Cus ome (c).closeAccoun (a) = Accoun (a).close = Ca d.in alida e(a); The global e en close(c, a) will be defined as: {(a [c.accoun ) ^(a.balance = 0) ^ (Vc d [Ca d.in alida e(a)} .c d.accoun = a )} close(c, a) {a [ /c.accoun ’} i.e., i mus be ulfilled ha he accoun a belongs o he cus ome c, ha his accoun has a balance equal o ze o and ha all ca ds associa ed wi h his accoun will be cancelled. The e en s ha can occu in each ins an will be ob ained. A global e en can occu in each ins an . I he e is mo e han one e en enabled, he elec ion will be non-de e minis ic. I no e en can occu , hen he sys em is blocked (in he case o non- e mina ing sys ems). 4 Example: he dining philosophe s’ p oblem The dining philosophe s’ p oblem will be specified using ou in e ac ion ope a o , al eady desc ibed in Sec ion 2. The defini i e class diag am is shown in Fig. 4. Since he numbe o philosophe s is i ele an , i can be supposed ha he e a e numPhil philosophe s (and, he e o e, he same o ks), being numPhil 52. Also a ibu es a e needed o deno e he cu en s a es o philosophe s and o ks. Le s p be he a ibu e o he philosophe s. I will be able o ake he alues { hinking, ea ing}. Le s be he a ibu e o he o ks. I will be able o ake he alues { ee, busy}. Local e en s a e akeFo ks and eleaseFo ks o he philosophe s, and isTaken and isReleased o he o ks. The beha iou o he classes Philosophe and Fo k is desc ibed by he ollowing ules: 1. {p.s p= hinking} Philosophe (p). akeFo ks {p.s p’=ea ing} 2. {(p.s p=ea ing)} Philosophe (p). eleaseFo ks {p.s p’= hinking} 3. {( =p. o kLe _ =p. o kRigh ) ^ .s = ee} Fo k( ).isTaken(p) { .s ’=busy} 4. {( =p. o kLe _ =p. o kRigh ) ^ .s =busy} Fo k( ).isReleased(p) { .s ’= ee} The fi s ule es ablishes ha a philosophe mus be hinking o ake his o ks. I he e en occu s, he phi- losophe will pass o ea . The second ule defines ha a philosophe p mus be ea ing in o de o elease his o ks. I his e en occu s, he philosophe will pass o be hinking. The hi d ule indica es when a philosophe can ca ch he o k . This o k mus be ee and also mus be a o k ha is on he le o on he igh o a philosophe whose iden ifica ion is passed as a pa a- me e . I he e en occu s, he o k will pass o be busy. Simila ly, he ou h ule es ablishes ha a o k mus be busy in o de o be eleased. When his e en occu s, he o k will pass o be ee. Two in e ac ions among objec s o he wo classes a e needed: 1. When a philosophe akes a o k, i mus disappea om he able (so ha ano he philosophe canno ake i ). Also, o a oid p oblems o deadlocks, a philosophe mus ake he wo o ks ha he needs a he same ime. 2. When a philosophe eleases a o k, i mus be a ailable on he able again. The philosophe mus elease he wo o ks ha he has a he same ime. The g aphical ep esen a ion o hese in e ac ions is shown in Fig. 5. The specifica ion o he in e ac ion cons ain s is as ollows: In e ac ion cons ain s ake(p): Philosophe (p). akeFo ks= Fo k.isTaken(p)[2]; elease(p): Philosophe (p). eleaseFo ks= Fo k.isReleased(p)[2]; end; As can be seen, each global channel has a pa ame e . I indica es he philosophe ha wan s o ake o o elease his o ks. Acco ding o defined in e ac ion cons ain s and lo- cal cons ain s imposed on each class (and ollowing he defini ions made in Sec ion 3.4), he global beha iou o he sys em is defined as ollows: {p e } ake(p) {pos } {p e } elease(p) {pos } whe e p e :(p.s p= hinking) ^(V [Fo k.isTaken . ( =p. o kLe _ =p. o kRigh ) ^ ( .s p= ee)) ^(#Fo k.isTaken = 2) pos :(p.s p’=ea ing) ^ (V [Fo k.isTaken . .s ’=busy) p e :(p.s p=ea ing) ^(V [Fo k.isReleased . ( =p. o kLe _ =p. o kRigh ) ^ ( .s p=busy)) ^(#Fo k.isReleased = 2) Fig. 4 Defini i e class diag am o he philosophe s p oblem Fig. 5 In e ac ion cons ain s be ween he classes Philosophe and Fo k pos :(p.s p’= hinking) ^ (V [Fo k.isReleased . .s ’= ee) He e, p econdi ion p e indica es ha he e en ake could happen i he philosophe p is hinking and he has wo ee o ks in his hands, he o ks a his le and a his igh . Pos condi ion pos indica es ha i he e en ake occu s, hen he philosophe p will be ea ing and he o ks ha he has in his hand will be busy. P econdi ion p e indica es ha he e en elease could occu i he philosophe p is ea ing and he has wo busy o ks in his hands, he o ks a his le and his igh . Pos condi ion pos indica es ha i he e en elease occu s, hen he philosophe p will be hinking and he o ks ha he has in his hand will be ee. 5 Conclusions and u u e wo k A flexible model o in e ac ion among objec s in which mul iple classes o objec s a e allowed o in e ac h ough a same e en has been p esen ed in his pape . E en s a e uni s o synch onisa ion and (n-way) com- munica ion among objec s. A specifica ion in ou model is made defining con- s ain s locally imposed on objec s. The global ision o a sys em is ob ained, defining he exis en in e ac ion cons ain s among objec s. Fo each class, all objec s sa is ying hei cons ain s will be able o pa icipa e in an in e ac ion. The imposi ion o global cons ain s on a sys em o on a pa o i (subsys em) may be ca ied ou by means o objec s keeping hese cons ain s locally. Fu he - mo e, hese objec s mus in e ac in a synch onous way wi h he es o he sys em. This pape con ains wo illus a i e examples: he dining philosophe s’ and he au oma ed banking p o- blems. We ha e made a specifica ion o he sys ems by means o ules ha define he possible ansi ions o s a e o he objec s composing hese sys ems. To gi e a global ision o each sys em, in e ac ion cons ain s ha e been defined. Finally, we ha e desc ibed he con- di ions ha ha e o be ulfilled in o de ha an e en o he sys em can occu . Ou in e ac ion mechanism has been implemen ed in wo diffe en ways: fi s ly using he LOTOS language [15] and secondly making an ex ension o he IP lan- guage [7]. This ex ension allows a dynamic numbe o p ocesses [17]. Ou u u e wo k is ocused on ob aining implemen a ions in an au oma ic way by means o me- chanisms o a lowe le el, as communica ion clien /se - e and ansac ions, which in a anspa en way assu e he same p ope ies as he o iginal specifica ion. We also plan o de elop a me hodology ha allows us o use in e ac ion cons ain s in a p ocess o so wa e de elopmen . Re e ences 1. Hoa e CAR (1985) Communica ing sequen ial p ocesses. P e- n ice-Hall In e na ional Se ies in Compu e Science, Engle- wood Cliffs, NJ 2. Milne R (1989) Communica ion and concu ency. P en ice- Hall In e na ional Se ies in Compu e Science, Englewood Cliffs, NJ 3. ISO (1989) In o ma ion p ocessing sys ems: open sys ems in e connec ion. LOTOS: a o mal desc ip ion echnique based on he empo al o de ing o obse a ional beha iou . ISO 8807 4. And ews GR (1991) Concu en p og amming: p inciples and p ac ice. Benjamin/Cummings, Redwood Ci y, CA 5. Jungclaus R, Ha mann T, Saake G (1993) Rela ionships be- ween dynamic objec s. In: In o ma ion modelling knowledge bases IV: concep s, me hods and sys ems. IOS P ess, Am- s e dam pp 425–438 6. Jungclaus R, Saake G, Ha mann T, Se nadas C (1996) TROLL – A language o objec -o ien ed specifica ion o in- o ma ion sys em. ACM T ansac ions on In o ma ion Sys ems, 14(2): 175–211 7. F ancez N, Fo man IR (1996) In e ac ing p ocesses: a mul i- pa y app oach o coo dina ed dis ibu ed p og amming. Addison-Wesley, Reading, MA 8. Booch G, Jacobson I, Rumbaugh J (1999) The Unified Mod- eling Language use guide. Addison-Wesley, Reading, MA 9. Rumbaugh J, Booch G, Jacobson I (1999) The Unified Mod- eling Language e e ence manual. Addison-Wesley, Reading, MA 10. Jonke s hbm (1999) Communica ion and synch onisa ion using in e ac ion objec s. Lec u e No es in Compu e Science, Vol 1709, pp 1321–1331 11. Manna Z, Pnueli A (1992) The empo al logic o eac i e and concu en sys ems: specifica ion. Sp inge , Be lin 12. Denke G, Ko ¨s e -Filipe J (1996) Towa ds a model o asyn- ch onously communica ing objec s. In: P oceedings o he second in e na ional Bal ic wo kshop on da abases and in o ma ion sys ems, Tallinn, p 182–193 13. Eugs e A, Gue aoui R, S en ek J (2000) Dis ibu ed asyn- ch onous collec ions: abs ac ions o publish/subsc ibe in e - ac ion. Lec u e No es in Compu e Science, Vol 1850, pp 252– 270 14. Man ˜as JA (1989) Dining philosophe s: a cons ain o ien ed- specifica ion. In: The o mal desc ip ion echniques LOTOS. Else ie Science, Ams e dam 15. To es J Objec o ien ed specifica ions based on cons ain s. PhD hesis, Depa men o Languages and Compu e Sys ems, Uni e si y o Se ille, Decembe 1997 16. Sounda ajan N (2001) Refining in e ac ions in a dis ibu ed sys em. Lec u e No es in Compu e Science, Vol 1871, pp 209– 220 17. Co chuelo R P o o yping dis ibu ed sys ems specifica ions based on cons ain s. PhD hesis, Depa men o Languages and Compu e Sys ems, Uni e si y o Se ille, Decembe 1999