From Automata Networks to HMSCs: A Reverse Model Engineering Perspective

Transcription

1 From Automt Ntworks to HMSCs: A Rvrs Modl Enginring Prsptiv Thoms Chtin,Loï Hélouët, nd Clud Jrd 3 IRISA/ENS Chn-Brtgn, Cmpus d Buliu, F-354 Rnns d, Frn Thoms.Chtin@iris.fr IRISA/INRIA, Cmpus d Buliu, F-354 Rnns d, Frn Loi.Hlout@iris.fr 3 IRISA/ENS Chn-Brtgn, Cmpus d Kr-Lnn, F-357 Bruz d, Frn Clud.Jrd@rtgn.ns-hn.fr Astrt. This ppr onsidrs th prolm of utomti strtion, from low-lvl modl givn in trm of ntwork of intrting utomt to high-lvl mssg squn hrt. This llows th dsignr to ply in ohrnt wy with th lol nd glol viws of systm, nd opns nw prsptivs in rvrs modl nginring. Our thniqu is sd on prtil ordr smntis of synhronous prlll utomt nd th onstrution of finit omplt prfi of n vnt-strutur oding ll th hviors. W prsnt th modls nd lgorithms. Th mpls prsntd in th ppr hv n prossd y smll softwr prototyp w hv implmntd. Introdution Dsigning distriutd pplition is ompl tsk. At th finl stg of th modling, on th diffrnt rhitturl disions hv n md, dsignrs usully otin st of ommuniting squntil omponnts. During rlir stgs of softwr dvlopmnt, dsignrs us mor strt nd visul rprsnttions suh s snrios. For instn, Mssg Squn Chrts (MSCs) [9] r n ppling visul formlism to ptur systm rquirmnts. Thy r prtiulrly suitd for dsriing snrios of distriutd tlommunition softwr [7]. Svrl vrints of MSCs ppr in th litrtur (squn digrms, mssg flow digrms, ojt intrtion digrms, Liv Squn Chrts) nd r usd in numr of softwr nginring mthodologis inluding UML [8]. Thy provid th dsignr with glol viw of th dynmi hvior of th systm, givn in dlrtiv mnnr. Howvr, thr is oftn gp twn th lol viw dfind s squntil omponnts nd th mor glol viw dsrid y snrios. Som snrios nnot implmntd y squntil mhins, nd som ompositions of s- F. Wng (Ed.): FORTE 5, LNCS 373, pp , 5. IFIP Intrntionl Fdrtion for Informtion Prossing 5

2 49 T. Chtin, L. Hélouët, nd C. Jrd quntil mhins do not hv finit rprsnttion in trms of MSCs. This is why lot of rnt works hv n dvlopd to utomtilly gnrt ommuniting utomt (t lst sklton) from MSCs [,5] in th ontt of top-down dsign mthodology. Oviously, uilding ridg in th opposit dirtion is lso n intrsting prolm, s it would llow dsignrs to ply frly with ny styl of spifition (glol dlrtiv or distriutd imprtiv) whil prsrving th ohrn of oth viws. A solution to this prolm ould lso th sis of nothr importnt hllng lld spt modling, in whih nw ftur dsrid s st of snrios n ddd sfly to n lrdy isting modl of ommuniting mhins. This will imply sophistitd forml thniqus, sin th rquird trnsformtions modify drmtilly th strutur of th utomt. This ontt motivts our work on som rvrs distriutd modl nginring. W gin with simpl modls, whih r ntworks of synhronous prlll finit stt utomt for th imprtiv spt, nd MSCs for th dlrtiv spt. Th prolm is thus to utomtilly otin MSC from n utomt ntwork, whih ods ll th runs of th systm, runs ing dfind s prtil ordrs of trnsition ourrns. Th finitnss of th utomt nd th synhronous ommunition nsur tht suh trnsformtion is possil. This qustion hs lrdy n ddrssd from th thortil point of viw in trm of forml lngugs in [3]. Thy show tht ny singl Bühi utomton with struturl proprty, lld dimond, nd with ll its stts pting, is l to gnrt th lngug of oundd MSC. Howvr, this prolm is undidl for synhronous ommuniting finit stt mhins. This justifis our hoi to onsidr synhronous ntworks nd to propos n originl lgorithm to produ onrt MSC, s rdl s possil. Figur shows n mpl of suh ntwork, whih onsists of two utomt A nd A, synhronizd on thir ommon vnt. Figur givs th orrsponding MSC w would lik to omput. Noti tht th MSC grph is ompl du to th ft tht this mpl ws dsignd to show ll th triky spts of th trnsformtion. A mor rlisti mpl is trtd in Stion 4. W will us th notion of unfolding, nd th ft it n finitly gnrtd y finit omplt prfi. This is sd on th unfolding thory, s prsntd in [4,]. In th ppr, w dopt nvrthlss dirt pproh, without using Ptri nts s usul, in ordr to void to introdu nw intrmdiry forml modl. Th qustion of using th finit prfi s gnrtor of th unfolding is lso nw up to our knowldg. Th rst of th ppr is orgnizd s follows. Stion dfins formlly utomt ntworks, MSCs nd th notion of runs. Th nt stion 3 is dvotd to th gnrtion of possil runs y th onstrution of finit omplt prfi of th unfolding. Stion 4 prsnts how th MSC utomton nd th rfrnd si MSCs r trtd from th prfi. W onlud y disussion summrizing th pproh nd proposing fw prsptivs. All th proofs of th propositions nd thorms r vill in th rsrh rport [].

3 From Automt Ntworks to HMSCs 49 hms Glol viw d d d ms A A ms A A ms d A A d ms A A Fig.. A ntwork of two synhronizd utomt nd its snrio viw Dfinition of Automt Ntworks nd MSCs. Ntworks An initilizd llld utomton is tupl A = S, Σ,, s whr S is finit st of stts, Σ is st of lls, S Σ S is st of llld trnsitions, nd s S is th initil stt. For trnsition t = (s,, s ), w dnot α(t) df = s its sour, β(t) df = s its trgt, nd λ(t) df = its ll. I df = {,..., n} dnots finit st of indis. W onsidr th synhronous prlll omposition of th initilizd llld utomt A i = S i, Σ i, i, s i i I Th ntwork of Figur is formlly dfind y: S = {,, } S = {,, } Σ = {,, } Σ = {, d,, } s = s = = {(,, ), (,, ), (,,), (,, )} = {(,, ), (,, ), (,,), (, d, )} In n intrlving smntis, th ntwork hvior is dfind s th (glol) initilizd llld utomton A = S, Σ,, s whr:

4 49 T. Chtin, L. Hélouët, nd C. Jrd S df = S S n Σ df = i I Σ i ((s i ) i I,, (s i ) i I) iff s df = (s,...,s n ) i {,..., n} i {,..., n} { (si,, s i ) i (s i = s i / Σ i ) (s i,, s i ) i d d d Fig.. Th synhronizd produt ms SynhroBrrir A B C m n o Fig. 3. MSC rprsnttion of rndz-vous Intuitivly, w for th utomt to volv synhronously whn thy ut trnsition llld y th sm nm. In th othr s, thy volv indpndntly. Figur shows th produt utomton of our mpl. Squntil runs r th diffrnt pths in th grph of th produt utomton. Unfortuntly, this notion of run dos not nlight th usl rltions twn th diffrnt ourrns of trnsitions (sn s tomi vnts), s don in MSCs. In our ontt, th right notion of run is th prtil ordring of vnts tht hv ourrd. Hn, runs of systm will dfind s si MSCs.. Mssg Squn Chrts MSCs r omposd of si snrios (or MSCs), tht dpit intrtions mong svrl ojts. Ths intrtions r thn omposd hirrhilly y

5 From Automt Ntworks to HMSCs 493 mns of oprtors (loop, hoi, squn,...). For th sk of simpliity, w will only onsidr singl hirrhil lvl. Intrtions in th utomt ntworks w onsidr r synhronous (i.. Rndz-vous ommunition): thy r loking, nd involv svrl prtiipnts. For this rson, ommunitions in MSCs will rprsntd y rfrns to othr MSCs dsriing how ommunition mhnism is implmntd. Suh Rndz-vous n implmntd using synhroniztion rrir, s dpitd in Figur 3. In MSCs, rfrning insid digrm is llowd y inlin prssions. Hr, w will only onsidr rfrns to simpl MSCs dpiting ommunitions mong givn st of omponnts. W do not llow rfrn nsting, nd will not us inlin prssions with opt, lt or loop. In our frmwork, MSC is dfind s finit st of vnts. Eh vnt is rprsntd s th vtor of its prdssors on h instn. Th sn of prdssor on n instn is dnotd y th null vnt. W ssoit ll to h vnt, whih will srv to not th orrsponding trnsition of th utomt. For mpl, onsidring systm with thr instns, th vnt 3 dnotd y ((, (,, )),, (, (3,, 4))) is synhroniztion vnt twn th first nd th third instn, nd hving th vnts nd s immdit prdssors on ths instns. Thr is no immdit prdssor on th sond instn sin it dos not prtiipt in th synhroniztion. Th lls r (,, ) nd (3,, 4), dnoting for instn th trnsitions to synhroniz in n utomt ntwork. Formlly, MSC ovr st of instns I is tupl B = (E, Σ, A, Θ), whr E = {( i, σ) i I, σ Σ} is st of vnts suh tht h i { } E Σ. E ontins lol vnts (vnts suh tht { i } = ) nd intrtions (vnts suh tht { i } > ). Σ is lol lpht, A is n lpht of lol tions nd intrtion nms, nd Θ : Σ A ssigns glol nm to vnts. Whn f i = (, σ), w dnot π i (f) =. W will sy tht is prdssor of f, nd writ f whn i I suh tht π i (f) =. E lso ontins spifi vnt = (,..., ) i I lld th initil vnt tht hs no prdssor. W will sy tht n vnt is miniml in MSC iff is th uniqu prdssor of ll its omponnts. A MSC must lso stisfy th following proprtis : i) th rfliv nd trnsitiv losur of is prtil ordr. ii) (synhroniztion) = ( i ) i I E, w rquir tht!, i I, i = Θ(σ i ) =. This proprty mns tht ll omponnts prtiipting to n vnt must synhroniz. iii) (lol squning) i I, E, i = π i () = or (π i ()) i iv) (no hoi) (, ) E, i I, = π i () π i ( ). This proprty forids th introdution of hois in MSC. MSCS r good ndidts to modl usl rltions in runs of distriutd systm. Cuslity twn vnts is dfind y. Whn nithr, nor, w will sy tht nd r indpndnt (or onurrnt). Th st of miniml vnts in B w.r.t is dnotd y min(e). W will sy tht n vnt is miniml for n instn i I if th prdssor vnt on omponnt i is. It is miml for this instn if it is not prdssor vnt for n vnt on this

6 494 T. Chtin, L. Hélouët, nd C. Jrd instn. Th miniml (rsp. miml) vnt on instn i (whn it is dfind) will dnotd y min i (E)(rsp. m i (E)). A MSC B is prfi of MSC B if nd only if E E nd E, Θ () = Θ (). Th mpty MSC is th tupl B = ({ },,, ). Figur 4 is n mpl of MSC. This MSC dfins th hvior of instns A nd A. Evnts,,, r lol tions, nd rfrn rprsnts synhronous intrtion twn A nd A. Th squntil omposition of two MSCs B = (E, Σ, A, Θ ), B = (E, Σ, A, Θ ) is th MSC B = (E, Σ Σ, A A, Θ), whr : E (E \ ( { } {min i (E ) i I} )) E = (,... n) i { I, (,..., n ) min i (E ) j I, j = (mj (E ), σ) if j = (, σ) j othrwis Θ(σ) = Θ (σ) if σ Σ, Θ (σ) othrwis Mor intuitivly, squntil omposition mrgs two MSCs long thir ommon instns s y ddition of n ordring twn th lst vnt on h instn of B nd th first vnt on th sm instn in B. A High-lvl Mssg Squn Chrt (HMSC) is tupl H = (N,, M, n, F), whr N is st of nods, N M N is trnsition rltion, M is st of MSCs, n is th initil nod, nd F is st of pting nods. HMSCs n onsidrd s finit stt utomt llld y MSCs. A HMSC H dfins st of pths P H. For givn pth p = n M M n n... M k n k P H w n ssoit MSC B p = M M M k. Th runs of HMSC H r th prfis of ll MSCs gnrtd y pths of H. Th run ssoitd to th mpty pth is B..3 Runs s Prtil Ordrs A run of n utomt ntwork A i = S i, Σ i, i, s i i I is dfind s MSC M = (E, Σ, A, Θ), with th following proprtis: i) Σ = i I i. Hn, for n vnt = ( i ) i I, h i is of th form i = (, t), nd w will dnot τ i () df = t, α i () df = α(t) nd β i () df = β(t). W dfin β i ( ) df = s i. ii) A = Σ i. i I iii) Θ(t) = λ(t) iv) (lol squning) i I i = α i () = β i (π i ()) As Σ, A, Θ r impliit for givn st of vnts E, w will oftn dnot MSC B = (E, Σ, A, Θ) y its st of vnts E. Intuitivly, n vnt rprsnts th synhroniztion of tions of th utomton A i suh tht i ; nd i = (, t) mns tht th lol tion on utomton A i is t, nd th

7 From Automt Ntworks to HMSCs 495 ms Run A A Fig. 4. A run s dfind s MSC with inlin rfrns prvious tion tht onrnd th utomton A i ws. Not tht proprty iii) implis tht for givn omponnt i I nd for ny hin = (, t ) = (, t )... k = ( k, t k ) suh tht j..k, j i, th squn t.t... t k is pth of utomton A i. This run orrsponds to th ontntion of th MSCs AB nd CEX of Figur. Its vnts r: =, 3 = ((, (,, )), ), = ((, (,, )), ), 4 = (, (, (,, ))), = (, (, (,, ))), 5 = ((3, (,,)), (4, (,,))) Th qustion now is to rprsnt ll th possil runs. This is th rol of th unfolding, whih suprimposs ll th runs, shrs th ommon prfis nd distinguishs th diffrnt historis using th notion of onflit. 3 Gnrtion of Runs 3. Unfolding W onsidr th union of ll possil runs, forming nw vnt st E. Th sn of hois is no mor gurntd. This is why w dfin th onflit rltion # on th vnts s follows: f f # iff f, f f E f i I π i (f) = π i (f ) Informlly, two vnts r in onflit if thy hv ommon nstor vnt tht rnhs on sm instn. Th unfolding of th synhronous prlll omposition of th initilizd llld utomt A i = S i, Σ i, i, s i i I is th st U of ll vnts tht r not in slf-onflit: U df = { E ( # )}. Grphilly, w drw irl for h vnt, nd n r from to, llld y i h tim i = (, t). Figur 5 shows th shp of th unfolding of th ntwork of Figur.

8 496 T. Chtin, L. Hélouët, nd C. Jrd d d d d d Fig. 5. Th unfolding of th ntwork of Figur nd its finit omplt prfi A (finit) run (lso lld onfigurtion) of th unfolding is MSC B = (F, Σ, A, Θ) whr Σ, A, Θ r dfind s usul, nd F { is finit sust of E whih is onflit-fr nd uslly losd,, f F ( # f) i.: f F E f = F Proposition. Th unfolding ontins ll th possil runs. 3. A Trivil Solution for MSC Etrtion As plind prviously, our gol is to omput glol dlrtiv viw dfind s MSC from distriutd imprtiv viw of distriutd systm givn y ntwork of utomt. Th istn of trivil solution to this prolm is gurntd y th following proposition. Proposition. Lt A = (S, Σ,, s ) th glol initilizd llld utomton otind y synhronous produt of utomt (A i ) i I. Lt H = (S, (Σ),, s, S) th HMSC whr (σ) is th MSC ontining singl lol tion prformd y n utomton or singl intrtion prformd y ll utomt involvd in synhronous ommunition, nd = {(n, (σ), n ) (n, σ, n ) )}. Thn, th st of runs of H nd th st of runs of (A i ) i I r quivlnt. W n imgin th rsulting HMSC y hving look on Figur. Clrly, it dos not fulfill our gol of rvrs modl nginring. W must try to fill s muh s possil th MSCs.

9 From Automt Ntworks to HMSCs Finit Complt Prfi Th unfolding U of n utomt ntwork is n infinit strutur. Howvr, it is possil to work on finit rprsnttion of U lld finit omplt prfi. For onfigurtion U nd for n utomton i I, w dfin th lst vnt i tht onrnd i in s th vnt f suh tht: (f i f = ) f π i (f ) = f Proposition 3. For onfigurtion U nd for n utomton i I, i is uniqu. W dnot, th vtor ( i ) i I of lst vnts. Th glol stt vtor ssoitd with onfigurtion is lso dfind s th stts of h utomton ftr hving prformd th vnt i, i.. GStt() df = (β i ( i )) i I For ll U, df = {f E f } is onfigurtion, lld th lol onfigurtion of. W dfin th st C of ut-off vnts of n unfolding s: C iff f \ {} GStt( f ) = GStt( ) Atully th vnt f for ut-off vnt is gnrlly not uniqu. W dfin th rgnrtion onfigurtion, dnotd of ut-off vnt C s th intrstion of th lol onfigurtions f of th vnts f \{} suh tht GStt( f ) = GStt( ): df = f \{} GStt( f )=GStt( ) f. Proposition 4. For ll C, GStt( ) = GStt( ). U. Th st { U f C f + } is finit omplt prfi of th unfolding Thorm. Th finit omplt prfi is finit gnrtor of th unfolding. Figur 5 (right) shows th prfi otind from our mpl. Lt us onsidr th vnt, llld y. It is ut-off vnt. Its rgnrtion onfigurtion is { }. This is grphilly rprsntd y n osillting rrow pointd to, knowing tht =.

10 498 T. Chtin, L. Hélouët, nd C. Jrd Th following lgorithm omputs th finit omplt prfi U. Initiliztion. rt th initil vnt: U = = ( ) i I, with GStt({ }) = (s i ) i I;. C ; Rpt until ddlok. slt tupl ( i ) i I whr { i { } i, suh tht: i = = / Σ Σ i I i i = λ i ( i ) = i I i = i U \ { C, β i( i ) = α i( i ) i = (. uild th vnt = ( i ) i I, whr i, i) if i i = othrwis 3. if / U ( # ) in U {} U U {}; if with GStt( ) = GStt( ): thn C C {}; f \{} GStt( f )=GStt( ) f 4 MSC Etrtion MSC trtion strts with th strtion of th prfi. Intuitivly, for givn finit omplt prfi, w dfin X s sust of onfigurtions tht ontins th lol onfigurtion of th ut-off vnts, thir rgnrtion onfigurtion, th lol onfigurtion of th trminl vnts, nd tht is losd undr intrstion. X n projtd on h instn in ordr to otin ntwork of strt utomt. Th produt forms th HMSC utomton. Bsi MSCs r otind y onsidring ll th vnts ouring in n intrvl twn two onfigurtions of X, nd trnsitions r ddud from onfigurtions inlusion. W dnot y P th finit omplt prfi of th unfolding U of n utomt ntwork. An vnt is trminl if thr ists no f U suh tht f. Lt X th st of onfigurtions indutivly dfind s: { } X for ll ut-off vnt, X X; for ll trminl vnt, X; for ll, X, is onfigurtion = X. W dnot y Y df = { C} th lol onfigurtions of ut-off vnts. df For ll X, lt us dfin E = \. Th sts E r susts of X lmnts tht r not ontind in ny smllr onfigurtion of X. Thy dfin th MSCs tht will trtd from th prfi.

11 For ll X, th sts E with X, r prtition of. For ll vnt w dnot E (, ) th uniqu onfigurtion X suh tht nd E. Lt us dfin n strtion of th prfi P, whr th lmnts of X ply th rol of mro-vnts. For ll i I w dfin th st X i of mro-vnts tht onrn i s: df X i = { X E, i = } For th mpl of Figur 5, w hv: X = {, d,,, } E =, E d = d, E =, E =, E = X = {,,, }, X = {, d, } Y = { d,, } For ll i I nd for ll X i \ {{ }}, th lst vnt tht onrnd i in \ E is i ( \ E ). W dfin th mro-vnt tht immditly prds on i s π i () df = E ( i ( \ E ), ). Using this dfinition, for h i I w n now dfin th initilizd llld mro-utomton whr From Automt Ntworks to HMSCs 499 df A i = X i \ Y, {E X i }, i, { } i = {(π i(), E, ) X i \ {{ }} / Y } {(π i (), E, E ( i, ) X i = with ut-off vnt} Figur 6 shows th ntwork of mro-utomt otind from our mpl. Lt A = S, Σ,, s th synhronous produt A A A n. Th HMSC trtd from finit omplt prfi P is dfind s H P = (S,, (Σ), s, S), whr σ Σ, (σ) is th MSC otind y dding s prdssor of ll miniml vnts to σ, nd = {(s, (σ), s ) s, σ, s ) }. For our mpl, th HMSC omputd from th synhronous produt in Figur 6 is th rsulting HMSC of Figur nnound in th ginning. Thorm. Lt P finit omplt prfi of n utomt ntwork unfolding, nd lt (A i ) i I th st of mro-utomt otind from P. Lt H th HMSC otind from th synhronous produt (A i ) i I. Th runs of (A i ) i I nd th runs of H r quivlnt. d d d Fig. 6. Th ntwork of mro-utomt nd its produt

12 5 T. Chtin, L. Hélouët, nd C. Jrd Lt us onsidr th mor rlisti mpl shown in Figur 7 (lft). It is simpl onntion nd rls protool twn two prs. Th two prs (sndr nd rivr) r prsntd on top of th figur. Thy r onntd through hnnls of siz on. Th utomt of hnnls r givn t th ottom of th figur. In this protool, th sndr n initit onntion y snding th Crq mssg (! nd? hrtrs dnot th snd nd riv tions rsptivly). Aftr tht, it n did lolly to los th onntion y snding th mssg Drq, or rivs th mssg Ddrq inditing tht distnt disonntion hs n md y th rivr. In s of ollision (rption of Ddrq in stt ), th onntion is lso losd. On th rivr sid, ftr hving rivd th Crq, th rivd my did to los th onntion y snding th distnt disonntion mssg Ddrq. If not, th Drq mssg is rivd in stt. In tht s, it is rquird tht th rivr lrts th sndr y th Donf mssg to llow it to los lolly th onntion. Not tht in s of ollision, it is possil to riv mssg Drq in stt, whih must skippd. 3?Crq!Crq?Drq 3?Donf?Ddrq!Crq?Ddrq!Drq!Donf?Crq?Drq!Ddrq?Ddrq!Ddrq 3?Drq?Ddrq!Drq 3?Drq 3?Crq!Crq!Drq?Drq?Ddrq!Ddrq!Donf?Donf!Crq!Donf?Donf Fig. 7. Th Connt-Disonnt protool with hnnls of siz on nd its prfi Figur 7 (right) shows th prfi of th unfolding of this mpl. W show thr ut-off vnts, orrsponding to th thr si pttrns of th protool, whih r lol disonntion, distnt disonntion nd ollision. Th MSC viw produd y our mthod is shown in Figur 8.

13 From Automt Ntworks to HMSCs 5 hms Glol viw!rq ms Ddis S SR RS R?Crq!Ddrq Dis Collid Ddis?Ddrq ms Collid S SR RS R!Drq?Crq ms Dis S SR RS R?Drq!Donf!Drq?Drq?Crq?Donf!Donf!Crq?Donf ms!rq S SR RS R!Crq Fig. 8. MSC trtd from Automt of Figur 7 5 Disussion W hv ddrssd th prolm of rvrs modl nginring, nd mor prisly th utomti trnsltion of synhronous ntworks of finit utomt into mssg squn hrts. A trivil solution is to uild th produt utomton nd to intrprt trnsition lls s si MSCs. Unfortuntly, this dgnrtd MSC dos not fulfill th rquirmnts of rvrs nginring, whih r to prsnt th onurrnt historis of th systm using s muh s possil prtil ordr viw. This work introdus nw thniqus tht prmit to rovr glol prtilordr sd viw of systm dsrid y omposition of squntil omponnts, nd hn sms rlvnt for rvrs modl nginring. Th min lgorithm is th unfolding of th ntwork of utomt. It omputs th st of ll prtil ordr runs. Thnks to th finitnss of th systm, this st is finitly gnrtd y prfi. From this prfi, w showd wy to trt si prtil ordr pttrns (MSCs). Th rmovl of ths pttrns in th prfi, followd y lol projtion ld to n strt ntwork of mro-utomt. A HMSC with th sm hvior s th initil utomt ntwork n thn produd y omputing th produt of mro utomt. An ltrntiv ould to onsidr prlll onstrut in th HMSC, s proposd for instn in nthrts [6]. Th lgorithms hv n implmntd in softwr prototyp ( fw thousnd of lins of C-od). Th nt stp will to l to dl with mor

14 5 T. Chtin, L. Hélouët, nd C. Jrd ompl systms. First, w hv to rl th synhronous ssumption to tk nfit of th synhronous ommunition in MSCs. W think it is possil to find lss of systms in whih synhronous ommunition n sfly rpld y n synhronous on without hnging th st of prtil runs. Lt us rll nvrthlss tht synhronous ommuniting utomt nd MSC dfin unomprl lngugs. This mns tht trnsltion of utomt into MSC my not ists. Furthrmor, diding whthr ntwork of synhronous utomt dfins MSC lngug is n undidl prolm. Hn, to fftiv in n synhronous frmwork, our pproh will nssrily pply to rstritd lss of utomt. Sondly, th MSCs w otin r dpndnt of two things: th dfinition of ut-off vnts nd th dfinition of onfigurtions tht r trtd from th finit omplt prfi. So fr, n vnt is ut off vnt if its onfigurtion hs lrdy n sn in its usl pst. This lds to som duplitions of vnts in th finit omplt prfi. Th dfinition of ut-off vnts n rfind using th dqut ordrs proposd y J. Esprz in []. This nhnmnt will rdu th duplition of vnts. Conrning th dfinition of onfigurtions to trt (th X st), w n did to shr mor or lss ommon prfis in th MSCs, nd find trdoff twn th numr of duplitions nd th siz of th onsidrd MSCs. This ould prmtrizd. Rfrns. L. Hélouët nd C. Jrd. Conditions for Synthsis of Communiting Automt from HMSCs, 5th Intrntionl Workshop on Forml Mthods for Industril Critil Systms (FMICS), ARE. Stfni-Gnsi, I. Shifrdkr (d), GMD FOKUS, Apr... J. Esprz nd S. Römr. An Unfolding Algorithm for Synhronous Produts of Trnsition Systms, Pro. of Conur 999, Ltur Nots in Computr Sin 664, pp. -, A. Musholl nd D. Pld. From Finit Stt Communition Protools to High- Lvl Mssg Squn Chrts, Pro. of ICALP, Ltur Nots in Computr Sin 76, pp. 7-73,. 4. K. M Milln. A Thniqu of Stt Sp Srh Bsd on Unfolding, Journl of Forml Mthods nd Systm Dsign, 9, - (99), Kluwr. 5. M. Adllh, F. Khnd, nd G. Butlr. Nw Rsults on Driving SDL Spifitions from MSCs, Pro. of 9th SDL Forum, pp. 5-66, Montrl. 6. M. Mukund, K.N. Kumr, nd P.S. Thigrjn. Nthrts: Bridging th Gp twn HMSCs nd Eutl Spifitions, Pro. of Conur 3, Ltur Nots in Computr Sin 76, pp. 96-3, E. Rudolph, O. Grumnn nd J. Growski. Tutoril on Mssg Squn Chrts, Computr Ntworks nd ISDN Systms - SDL nd MSC, Vol. 8, G. Booh, I. Joson nd J. Rumugh. Unifid Modling Lngug Usr Guid, Addison-Wsly, ITU, Mssg Squn Chrts, stndrd Z.,.. C. Jrd, L. Hélouët nd T. Chtin. From Automt Ntworks to HMSCs: Rvrs Modl Enginring Prsptiv, INRIA/IRISA Rsrh Rport, Aug. 5, pgs.