A Flexible and Executable Approach to Specify CSMA/CD Real-time Protocol and its referred Critical Properties

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1 A Flexible and Execuable Appoach o Specify CSMA/CD Real-ime Poocol and is efeed Ciical Popeies Mohamed Labi Rebaiaia Depamen of Compue Science, Bana Univesiy, Bana, Algeia. Absac We popose a fomal implemenaion and analysis ways o specify and veify eal-ime sysems. The heoeic model is adaped using synchonous imed-auomaa as a geneic famewok based on Timed Pocesses Algeba (TPA) o descibe is saic sucue and dynamic behavio. The absacion is povided by Maude [], exended o Real-Time Maude a fomalism and a simulaion and analysis ool fo eal-ime sysems. I has flexible specificaion fomalism, wih a naual inegaion of daa ypes, funcional aspecs and dynamic behaviou. I also has a wide ange of analysis capabiliies, including simulaions of single behavious and exhausive sae space exploaion saegies.. We addess he fomal specificaion of he CSMA/CD poocol as an execuable specificaion pogam o capue essenial opeaion aspecs and synchonous communicaions. The simulaion suppo imeous, wachdogs and abiay ime domains. We inoduce he efinemen aspec of an implemenaion ino a specificaion by axiomaizing he bisimulaion elaion. Key-Wods: Specificaion, Veificaion, Real-Time Sysems, Timed-Rewiing Logic, Maude Language, Pocess Algeba, CSMA/CD poocol.. Inoducion The Caie Sense, Muliple Access wih Collision Deecion poocol (CSMA/CD), is widely used on LAN s in MAC sublaye. Such sysem consiss of a medium and muliple finie numbe of sendes. Modeling he CSMA/CD poocol equies disceeime domains allowing evens o happen abiay and concuency semanic o povide he paallel composiion of he medium and he sendes. Such sysem can be appoached fomally as a imedauomaa. Timed auomaa povide a fomal model appoach fo eal-ime sysems. They ae addiionally consained by iming equiemens as invaians o geneae imed sequences and poceed wih finie conols-- a se of saes and a se of clocks []. The clocks measue he elapse ime a each level of he sysem. In he heoy, a lage numbe of echniques have been used fo modeling imed-auomaa funcionaliies, essenially he eseach woks of Henzinge e al [], [6]. A naual way o descibe concuen eal-ime sysems is o use Timed Pocess Algeba (TPA) [] as a sucual opeaional semanics. The TPA heoy leads o make exension and hus o conside he occuences associaed wih inevals of ime and give i a ansiion sysem semanic. Such semanic is used as mahemaical poofs ules. Real-ime sysems behavioal is given in he mos case using a saic fom of equaional logic and infeence ules in he fom of Bikoff equaional sysem. Fom his poin, using ewie sysems (dynamic inepeaion) and equaional logic (saic inepeaion), Mesegue e al [4], [0], [] have inoduced a new fomalism called Rewiing Logic. Such new concep, models boh saic and dynamic (sequenial and concuen) behavioal by using a sequence of seps and pemis he expessiveness of he ime as an acion. In his sense ewiing logic can be compaed and unified wih he specificaion of poblems based on pocess algebas as CCS [3], CSP [7], ACP [3] and ohes fomalisms like UNITY of Chandy and Misa, ACTORS of Agha, Pei nes, linea logic and empoal logics as he µ-calculus. To expess he easoning powe of ewiing logic, Mesegue e al have wien he inepee Maude based on OBJ3 [0] used as sub-language developed by Goguen s eam, a Edinbugh Univesiy. Maude language faciliaes he noion of communicaion synchonous and asynchonous ones as used in CCS [9] and gives an efficien fom ha could be aced o follow each execuion sep. A coninuous and exended gave been ealized by Olveczky e al [4] o appehend he noion of iming chaaceisic o model he equiemen of eal-ime concuen sysem in em of absacing he ime as a fomal quaniy. The appoach aken hee gives an oveview fo he expessiveness of he Timed Rewiing Logic (TRL) fo modeling eal-ime sysems. We invesigae he quesion of how i can be possible o easoning wih auomaic and symbolic veificaion sysems using ewiing logic ules as pesened in able. This pape is oganized as follows: CSIT006, Amman-Jodan, Apil 5 h Apil 7 h, Vol. ()

2 Secion deals wih he eal-ime sysems as model which can be specified as an algebaic dynamic specificaion [4]. A heoeical backgound and some popeies concening eal-ime sysems ae pesened. In secion 3, we inoduce Mesegue's Rewiing Logic and Maude as a specificaion Language. Secion 4 give a apid descipion of he synax and he semanic of some eal ime fomalisms and heis epesenaion in Maude Language. Finally, in secion 5 we explain how ewiing could be used fo he veificaion and simplificaion of eal ime sysem using he noion of bisimulaion.. The fomal model fo Real Time Timed labelled ansiion sysems povide a semanic famewok fo modelling eal-ime, faul-olean and hybid sysems. Such absacion is aken as a model M = (S, L, ) whee S epesens he ses of saes o nodes, L is he se of labels values aken fom a imed domain o names of acion A. The elemens in S can be eached saing fom s 0 he iniial sae and consiues he inemediae ineesing saes in he life of he Sysem. While ansiion elaion '' " descibes he capabiliies of he sysem o pass fom one inemediae sae o anohe one. A ansiion s l s means ha when he sysem is in he sae s, i is able o pass o he sae s by pefoming a ansiion whose ineacion wih he exenal wold is descibed by he label l which povides infomaion on he condiions of making effecive he possibiliy of he changes in he exenal wold caused by his ansiion. A ace is defined o be an infinie sequence of saes. Each pogam vaiable maps a given sae o a value of he vaiable in ha sae. Time is a special pogam vaiable whose value is no modified by a pogam. A behaviou is a ace whee he value of ime is nondeceasing and evenually inceases above any bound (non-zenoness) []. A sae pedicae is a poposiion ha is eihe ue o false fo each sae. A pogam is ypically given in ems of an iniialisaion sae pedicae and a se of aomic acions. A eal-ime sysem is a iple ha consis of a clock consain sysem and a delay pedicae he envionmen condiion of S. The ansiion condiion of he ealime asses necessay condiion on sysem acions. The envionmen condiion asses sufficien condiion on sysem acions. Fomal mehods and equaional logic, inoduces he noion of absac daa ype, algebas, sos, signaue, specificaion, model, - equaions, saisfacion, many-soed, ode soed _ hidden soed, and ohes ems. Fo insance when declaing he absac daa ype, he synacic pa of he algebas is capued by declaing names of sos and opeaions and his declaaion is giving by signaue (fo all hese commens see [4], [], [5], [0]). 3. Pogamming Pinciple in Timed- Maude Maude language is an objec-oiened and execuable specificaion based on ewiing logic ha is a flexible and expessive absacion in which diffeen models and concuen sysems can naually be specified. In Maude, concuen objec-oiened sysems can be defined using modules inoduced o he sysem Maude ino hee kind of modules: () a funcional module inoduced by he key-wod f-mod () a sysem module inoduced by he key-wod mod (3) and an objec-oiened module inoduced by he keywod omod. A module conains so and subso saing he diffeen sos of daa manipulaed by he module and how hose sos ae elaed. Maude's ype of sucue is ode-soed [0]. The naual law of Maude is o specify concuen and dynamic sysems inepeaion by means of a configuaion (sae) as a collecion of objecs and messages using he A.C.I (Addiive, Commuaive and Ideniy) opeao and he neual elemen. The objec of a class is a em of he fom : <O: C a : v... a n : v n > wih O as objec name, C as objec class, a i as he name of he aibue numbe i and v i he value of he aibue i. The sysem evolve by a paallel and condiional ewiing ules which ake he foms: cl [label] M,..., M n <O :C a s >... <O m :C m as n > <O i :C i as i >... <O ik :C ik as ik ><Q :D as >... <Q p : D p as p >M,..., M q if condiion A ule of his kind expesses a communicaion even in which n messages and m disinc objecs paicipae. To be pefomed he messages M,..., M n ae consumed and new messages M,..., M q ae ceaed and sen. The objecs occuing on he lefhand side ae deleed, and hose occuing on he igh side ae ceaed (Q,, Q p ). The objecs occuing on boh sides change hei local saes. The condiional Condiion is an opional condiion ule o guad conolling he applicaion of he ule. In Timed- Maude he ewie ules ake zeo o ime unis o be pefomed. Cl [ule]: means condiional ule and he em ule in [ule] is a label. In case of a simple ule we wie l wihou [ule]. Fo insance we declae he following absac daa ype by means of a funcional module : fmod bank_opeaion is Poecing In. So In, Na, Accoun, Msg Subso Na < In Class Accoun. a solde : Accoun Na. CSIT006, Amman-Jodan, Apil 5 h Apil 7 h, Vol. ()

3 msgs cedi, debi : Accoun Na Msg. msg ansfe_fom_ o _ :Na Accoun Accoun Msg vas C C : Accoun, va mon :Na. endfm Le us now give a simple example o explain he pogamming language Maude by means of objecoiened modules. The example pesens bank opeaions in em of balancing fom cedi o debi and vice-vesa of wo accouns say Cusum (C) and Cusum (C). The example can be pesened as synchonous and asynchonous ules whee (ansfe Mon Fom C o C), cedi(c, Mon) and debi(c, Mon) ae messages. The following cases descibe he synchonous and asynchonous ules :. Case: Synchonous ule: cl [ule] (ansfe Mon Fom C o C) < C: Accoun solde: S>< C: Accoun solde: S> < C: Accoun solde: S-Mon>< C: Accoun solde: S + Mon> if ( S Mon 0 ) Case: Asynchonous ules: cl [ule3] cedi(c, Mon) < C: Accoun solde: S > < C: Accoun solde: S-Mon> if S Mon 0 l [ule4] debi(c, Mon) < C: Accoun solde: S> <C: Accoun solde: S + Mon>. Rewiing logic is a fomal famewok based on boh ewie heoy and equaional logic which gives a igoous expessiveness and a good inegaion of eal ime sysems. A signaue in his logic is a pai of (, E) wih a anked alphabe of funcion symbols and E a se of -axioms. Given a signaue, he senences ae sequens of he foms [] E [ ] E wih and ae -ems. A heoy in his logic is a ewie sysem S = (, E, L, R) ; his genealises he usual noion of heoy, which is ypically defined as a pai consising of a signaue and a se of senences. When specifying eal-ime sysems, a ime domain saisfying geneal axioms is needed. We hen define a paamee called he ime. The esul of ime acion is consideed as simuli s and is specified using a ewie ule. Many auhos have used he noion of monoid sucue[] o model ime absacly. Fo example he aihmeical monoid, he commuaive monoid and in geneal wha we call he lef-cancelaive ani-symmeic monoid []. In many cases, ime is absacly modelled using he naual numbes N; in his sense we speak abou discee ime. Many auhos have showed ha discee imed models ae decidable []. Coninuous models ae modelled using he eal numbes R. Such imed models ae mosly non-decidable []. In his pape we assume ha ime akes values fom he naual numbes and declaed as so ime. So o deal wih he noion of ime we inoduce definiion as follows: Definiion. A imed ewie specificaion R is a iple R = (, E, R) whee (, R) is a imed specificaion and R is a se R T (X)ime (T (X) s (T (X)) s. (T (X)) sn, s, s, s,, s n sos( ). Elemens of R ae called ime ewie ules and use he noaion u = v u n = v n fo (,,, u, v,, u n, v n ) and if n = 0. Le S be a ewie heoy we say ha S enails a sequen [] [ ] and wie S - [] [ ] if and only if [] [ ] can be obained by finie applicaion of he deducion ules of he Table. Table. Deducive ules in Timed Rewiing Logic 0-Timed Reflexiviy. Fo each f n, n N, 0 Timed Tansiiviy. Fo each,, 3 T (X) and, R + we have he ule, Synchonous Replacemen. Le, u T (X), le {x,,x n } = FV() FV(u) and le {x i,,x i } = FV() FV(u) be he feevaiables of and u. Fo each,, n, u,, u n T (X) and R + we have he ule : [ ] [ u ], [ ] [ u ]...[ ] [ u ] i [ (,..., n )] [ u ( u,..., u n )] Timed Compaibiliy wih =. Fo Fo each,, u, u T (X) and, R + we have he ule [ ] = [ u ], [ ] = [ ]...[ u ] [ u ], u = [ i ] [ 4. Synax and Semanic of Real-Time Sysems Following he assumpion above, we absac he behavio of a eal-ime sysem an appoach based on auomaa using a fomal descipion as a labeled ansiion sysems (S, L, s 0, ) whee s 0 S (he iniial sae), L = Ac Time and Ac = A Ā he se of acion names and Time is he se of imed names anged ove d. The se A is anged ove a, b, c, he visible acions and ι A is said he invisible o hidden acion. The ansiion s ae labeled by he names of acions belonging o he se Ac o by posiive imes epesening he passing of ime. In his secion we pesen he synax and semanic of he specificaion language in em of a vesion of imed pocess algeba as given in Timed CCS, Timed ] in ik CSIT006, Amman-Jodan, Apil 5 h Apil 7 h, Vol. ()

4 CSP, Timed ACP and ATP []. The se of pocess expession is given by he following synax: X is a counable infinie se of pocess vaiables, d is a ime paamee and H is a subse of he se Ac. The communicaion pocess is defined by a a = a 3 which defines he communicaion funcion and a a = means ha a and a canno communicae o ineac. Tems in ha sense ae called he se of ems poduced by he gamma saing a he non eminal S such ha pocess name appeaing in he igh-hand side of an equaion belongs o {x,x,, x n }. In addiion evey ecusive insaniaion of a pocess is guaded by an acion o by a ime-ou o a wachdog consuc and ecusion is no allowed hough, esic_in and wachdog(). A. Time domain The ime consideed hee is aken in an absac way in ha sense o be used as a paamee o expess consains abou insans of occuences of an acion. Definiion. A ime domain is a commuaive monoid (D, + 0) saisfying he following equiemens:. d + d = d d = 0. lef-cancellaive: d + d = d + d d = d 3. ani-symmeic: (d + d = 0) d = d 4. he peode defined by d d d / d+ d = d is a oal ode. The following popeies can easily be poved as follows: (i) 0 is he leas elemen of D, (ii) fo any d, d, if d < d, hen elemen d such ha d + d = d is unique. I is denoed by (d d). We denoe D {0} by D*. We also wie d < d insead of d d d d. D is called dense if d, d : d < d d : d<d <d, D i is called discee if d, d : d<d d : d < d d < d. Since he ode is oal. Thus any elemen of D can be obained fom 0 by adding many successos of 0. Example of ime domains: he naual numbes (discee domain), Q + and R + (dense) o enen he singleon {0}. B. Time deeminism I is usually admied ha when a pocess P is idle (does no pefoming acion) fo some duaion d, he esuling behavio is compleely deemined fom P and d (duaion). Thus he pogess of ime can be expessed by: P, P, P, d : P d P, P d P P = P Whee = is he synacic equaliy. C. Time addiiviy In ode o ensue he soundness of he noion of ime, i is usually equied ha: (i) a pocess which can idle can idle fo d + d ime unis, can idle fo d and hen fo d ime unis, and vice-vesa. (ii) in boh cases he esuling is he same. The popey of ime addiiviy (pesened in all he pocess algebas excep U-LOTOS) is fomally defined by : P, P, d,,d : ( P : P d P, P d P ) P d+d P The ime addiiviy axiom is appehended by he ansiiviy ule of TRL (see able ). As we have seen above, ime is modelled absacly by a commuaive monoid (Time,+, 0) wih addiional opeaos,, and he monus opeao -- saisfying Maude heoy. Using Maude language, we can specify he so Time as follows: fh TIME is poecing Bool. poecing Time. so 0 : Time. op _+_ : Time Time [assoc,comm., id: 0]. ops _<_, _ _: Time Time Bool. ops _--_ : Time Time Time. vas x, y, z, w,,,, d, d, d : Time. ceq d=0 if (d + d ) == 0. Ceq d = d if d+ d == d + d. eq (d+d ) d =d. ceq d d = 0 if no( d d ). eq d d + d = ue. ceq (d d ) = ue if (d == d ). eq (d < d) = false. eq (d d ) = (d < d ) o (d=d ). ceq d + d d + if d d and d. ceq (d d) + d = d if d d. endfh In he above heoy i can be poved ha he elaion _ _ is a paial ode, ha fo all d,d : Time, 0 d = ue, and ha d d if and only if hee exiss a unique d (namely d-d ) such ha d = d + d. D. Declaing so, subso and opeaion in Maude The pocess algebas ae defined by a se of em and opeaion on his se. In Maude Language i is possible o declae opeaions o opeaos on he sos as much as we need. To ealize such opeaions, we need o begin by he key-wod op followed by he name of he opeao and he funcional fom of he elaion beween he ems o sos and subsos. The pocess algebas used in such case allowed o declae he following opeaions : sos pocesse, acions. subsos pocess < pocesse, acion < acions. op _: pocess pocess Time pocesse op _: pocess pocess Time pocesse op Γ : pocess acion pocesse op : pocess pocess pocesse op _ _: pocess pocess pocesse CSIT006, Amman-Jodan, Apil 5 h Apil 7 h, Vol. ()

5 op _ _: pocess pocess pocesse op δ : pocess pocess Time pocesse The semanic if he language is given as a Sucued Opeaional (SOS). The meaning of he specificaion is defined by he infeence ules as follows : Specifying Time-ou infeence ules semanic ceq (P, Q, ) P if P P. ceq (P, Q, ) (P, Q, ) if = = +. eq (P, Q, 0) 0 Q. ceq Γ( (P, Q, d), a) d P if Γ(P, a) P. ceq (P, Q, d) d (P, Q, d ) if P d P and d = = d + d. ceq (P, Q, d) d Q if P d P and P d P and d = = d + d. Specifying Wachdog infeence ules semanic ceq Γ( (P, Q, d), a) (P, Q, d), if Γ(P, a) P and no(a = cancel). ceq (P, Q, d) P if P d P. ceq Γ( (P, Q, d), ho) d P if Γ(P, cancel) P. ceq Γ( (P, Q, d), a) d Q if P d P and Q d Q and d = = d + d. ceq (P, Q, d) d (P, Q, d) if P d P and d = = d + d. Specifying he non-deeminism choice Wachdog infeence ules semanic The non-deeminisic choice P Q behaves eihe like P o like Q. In Maude language his i is expessed by he following infeence ules : ceq Γ( (P, Q), a) P if Γ(P, a) P. ceq Γ( (P, Q), a) Q if Γ(Q, a) Q. ceq P Q d P Q if P P and Q Q. Specifying he paallel composiion P Q: allows P and Q o poceed independenly and in addiion i allows compuaion beween hem. If P can pefom a Ac and Q can pefom b Ac,hen P Q can pefom he acion a b Ac. When P and Q canno synchonise, his siuaion is noed as a b = []. In his case he pocess P Q can wai a ime d if and only if boh P and Q can wai d ime. The specificaion pefomed such as : ceq Γ((P Q), a) P Q if Γ(P, a) P. ceq Γ((P Q), a) P Q if Γ(Q, a) Q. ceq Γ((P Q), a b) (P Q ) if Γ(P, a) P and Γ(Q, b) Q and no(a b) =. ceq P Q d P Q if P d P and Q d Q. Specifying Times so ime. op ime: Time Time. l ime( + ) ime( ). Specificaion of he CSMA/CD poocol The infomal specificaion of he CSMA/CD poocol is, when a saion has daa o send, i fis lisen o he channel. If i is idle, he saion begins sending is message. Howeve, if i deecs a busy channel, i wais a andom amoun of ime and hen epeas he opeaion. When a collision occus, because seveal saions ansmi simulaneously, hen all of hem deec i., abo hei ansmission immediaely and wai a andom ime o sa all ove again. If wo messages collide hey ae boh los. The popagaion delay of he channel plays an impoan ole in he pefomance of he poocol. The specificaion of he CSMA/CD poocol is pesened as a connexion beween he medium a one side and all he sendes a he ohe side. Fo ou case we will ake ino accoun jus he sende and wo sendes. Such siuaion is modelled in Maude language as follows : <S: sende> <M; medium> <S: sende>. We declae he class of sendes, and he class of medium as a mulise and muliaibue. We noe, ha he following specificaion didn a all epesens he oaliy of he CSMA/CD specificaion, bu jus he imed auomaon of he sende. Class sende as sae: s, acion : pos, x : value. Class medium as sae : m, acion : pos, y : value. mess send_, eady_, busy_, end_, cd_ : mesg. l < S, sende sae :s, acion: ini, x: 0> < S, sende sae :s, acion: send, x: 0>(send_). l < S, sende sae :s, acion: send, x: 0> (eady_) < S, sende sae :s, acion: eady, x: 0> (busy_) < S, sende sae :s4, acion: busy, x: 0>. l < S, sende sae :s, acion: send, x: 0> (begin_) < S, sende sae :s3, acion: begin, ime(lambda)>. l < S, sende sae :s3, acion: send, x = 0 >(begin_) (< S, sende sae :s0, acion: end_, ime(0)>, < S, sende sae :s4, acion: cd_, ime(lambda)>, _sigma). l < S, sende sae :s4, acion: cd_, x = 0 >(cd_) (< S, sende sae :s, acion: end_, ime(0)>, < S, sende sae :s4, acion: cd_, ime(_sigma)>, _sigma). 5. Sysem Equivalence using Bisimulaion CSIT006, Amman-Jodan, Apil 5 h Apil 7 h, Vol. ()

6 Fo he veificaion of heoeical esuls, he noion of inducion pinciples is needed. Much ofen we need o efine he implemenaion much moe unil o obain a specificaion moe acable o be used diecly. Such siuaion is povided in em as an absac daa ype wih a sepaae equivalence elaion. We invesigae he possibiliy of obaining mechanical suppo using Maude Language fo equaional easoning in pocess algeba and o obain a famewok fom he efinemen of he implemenaion of a case sudy ino specificaion. In famewok, pocesses ae epesened by ems consuced fom aoms and opeaos and axioms specifying which pocess ems ae consideed o be equal. The idea povided a good aemp o simulae he behavio of Maude inepee as a mechanical poof-checke like PVS o Coq o Spake. Such famewok allows expeimens wih ools suppo on pocess algeba applied o eal-ime sysems. Definiion 3. A elaion R ove pocess expessions (i is assumed o be well-fomed and egula as in []) is a imed bisimulaion iff P R Q implies, fo all σ. Wheneve P σ P hen fo some Q, Q σ Q and P R Q. Wheneve Q σ Q hen fo some P, P σ P and P R Q. To illusae he main concep of bisimulaion. I was shown in [], ha pocess algeba can be pesened by a se of he following axioms (we wie he min Maude). We fis declae ha he lef mege opeao as a lef paallel opeao hen we declae he pocess Nil which is he empy pocess which does nohing. Op _ _: pocess pocess pocesses The axioms: eq P Q = Q P. eq P Q R = P (S R). eq P P = P. eq (P Q). R = P. R Q. R. eq (P Q) R = P R Q R. eq a P = a. P. eq a. P Q = a. (P Q). eq (P Q) R = P (Q R). eq P Q = P (Q R). The se of axioms pesened above can be exended o imed axioms as follows : eq d.(p Q) d = d.p d. Q., eq (d + d). P = d. d. P. eq (Null). P = P. ***Null : Duaion = 0 ime uni I was shown by a numbe of auhos, ha he se of axioms pesened above ae sound and complee. Using he axioms pesened above, we can povide a famewok o simplified he implemenaion o obain a complee specificaion. 6. Conclusion In his pape,we have pesened a mehodology fo specifying, designing and easoning abou eal-ime sysems. Ou goal was o show ha exising models of concuency as eal-ime sysems can be specified using ewiing logic. The modelling is pefomed using algebaic mehodologies as Timed CCS and ATP as developed by Sifakis e all. We have used Maude language as a famewok o wie specificaion and o do some expeimenaions and obaining execuions of a case sudy epesening a CSMA/CD poocol. We have shown ha simplificaion and minimizaion of he sucual fom of he bahavioal of he model, epesening he specificaion is pefomed using wha we call bisimulaion, in em of a se of sound and complee axioms. 7. Refeence [] L. Aceo, A. Jeffey, A Complee Axiomaizaion of Timed Bisimulaion fo a class of Timed Regula Behavios. TCS 5, 5-68, 995. Elsevie. [] R. Allu, T. A Henzinge, P. H Ho, Auomaic Symbolic Veificaions of Embedded Sysems. Jounal of IEEE Tansacion On Sofwae Engineeing, (3), Mach 996. [3] J.A Begsa, J. W Klop, Algeba of CSP wiih absacion. TCS 37 (), 77-, 985. [ 4] E. Coscia and G. Regio, Deonic Conceps in he Specificaion of Dynamyc Sysems The Pemission Case. TR, DISI-TR Dipaemeno di Infomaica e Scienze dell Infomazione. Univesia di Genova, Ialy,995. [5] V. Glabeek, W. P. Weijland, Banching Time and Absacion in Bisimulaion Semanics. Jounal of ACM, Vol 43 (03), May 996, PP [6] T.A. Henzinge, X. Nicollin, J. Sifakis, S. Yovine, Symbolic Model Checking fo Real-Time Sysems, Infomaion and Compuaion (): 93-44, 994. [7] C.A.R. Hoae, Communicaing Sequenial Pocess. Penice Hall,London,985. [8] P. Janca, F. Molle, Techniques fo Decidabiliy and Unecidabiliy of Bisimilaiy..Concu 999. [9] R. Milne, A Calculus of Communicaion Sysems. Spinge LNCS 9, 980. [0] J. Mesegue, A Rewiing Logic as a Unified Model of Concuency. LNCS, Concu 990. [] J. Mesegue, Rewiing Logic and Maude: Conceps and Applicaions. In L. Bachmai, edio, R T A, volume 830, LNCS, 000. [] X. Nicollin and J. Sifakis, An oveview and synhesis on Timed Pocess Algebas, Poceeding 3d CSIT006, Amman-Jodan, Apil 5 h Apil 7 h, Vol. ()

7 wokshop on compue-aided veificaion, Albog, Denmak, July 99 [3] R. Milne, A Calculus of Communicaion Sysems, Spinge LNCS 9, 980. [4] P. C. Olveczky, J. Mesegue, Specifying Real- Time Sysems in Rewiing Logic. ENTCS 4 (996). [5] M. L. Rebaiaia, K. Benfifi, B. Rezki., F Abdellaoui, S. Mousai., VERIF: An Auomaic Specificaion and Veificaion Tool fo Indusial and Reacive Sysems. Poceeding of he ACIT0 confeence, Jodan, 00. [6] M.L. Rebaiaia and J. M. Jaam, VALID-: A Pacical Modeling, Simulaion and Veificaion Sofwae fo Disibued Sysems. In he poceeding of he IEEE-IPDPS 004, Sana Fee, New Mexico, Apil. CSIT006, Amman-Jodan, Apil 5 h Apil 7 h, Vol. ()