N tie b P3 {1} some_action(1) T2. some_action(1) b (1),b+(1) P1 {1,2} an_action T1. an_action b+(x) P4 {1} P6 {1,2} x 1. b (1),d+(2) d+(2) {dot} {dot}

Transcription

1 New Petri Net Progrmming Fetures in PEP? Cecile Bui Thnh nd Christin Stehno 2 Universite Pris 2, LACL, 6 venue du generl de Gulle F-9400 Creteil, Frnce. ui@univ-pris2.fr 2 Deprtment of Computing Science, Crl von Ossietzky Universitt, D-26 Oldenurg, Germny. stehno@informtik.uni-oldenurg.de Astrct. We present two new fcilities of the high level Petri net editor of the PEP tool. The ltest version etends the clss of supported Petri nets y time etension of M-nets. Additionlly it fetures new opertor for synchronous communiction complementing the synchroniztion opertor. We present n emple of n ARQ protocol with enhnced cknowledgment hndling. form. Introduction The PEP tool [5, 9] provides development environment for numer of different prllel progrmming nd speciction lnguges. Additionlly, the high nd low level Petri net levels oer nother, quite unique, progrmming interfce. Especilly the high level nets fcilitte design of dt hndling lgorithms nd comple progrms through their etended token types nd powerful set of opertors. The ltest etensions of the net editors dd mjor new fetures with the introduction of new sic opertor tie nd new clss of nets, nmely the Time Petri net etension of the lredy used M-nets. This pper presents the enhncements of the speciction nd progrmming process gined y these etensions. The emple chosen for this purpose is simple ARQ (utomtic repet request) protocol with possily deferred cknowledgements. The net two sections will introduce the formlisms used for the emple, i.e. (Time) M-nets nd the tie opertor. In Sect. 4 the emple is presented, nd nlly in Sect. 5 the pper is concluded nd some future work is highlighted. 2 M-nets nd Time M-nets We will only give short introduction to M-nets nd their time etension. More detils cn e found in the cited ppers nd relted rticles.? This work hs een done during three month visit of one of the uthors to Oldenurg, nd hs een prtilly supported y the Procope project PORTA (Prtil Order Rel Time Semntics)

2 The coloured Petri nets lger of M-nets (multi lelled nets [2]) hs een developed s eile semntic model for concurrent progrmming lnguges. The nnottions of the net elements nd set of opertions provide frmework for the compositionl cretion of comple nets. Opertions include sequentil, prllel nd lterntive composition, itertion nd synchronous communiction y synchronistion nd restriction. Unfolding into plin P/T nets provides possiilities for forml veriction of the designed systems y mens of well-known lgorithms for ordinry Petri nets, e.g. with the PEP tool. Time M-nets (TM-nets) re cutious, ut still sustntil etension of M- nets towrds rel-time systems. The time etension ws originlly dened in [4] for rel-time version of the speciction lnguge SDL. TM-nets hd een supported so fr only in the MOBY tool [] without possiility to vlidte the nets. The newly implemented TM-net fetures of the PEP tool, together with the lredy presented nlysis tools for timed systems [2, 3] increse the importnce of TM-nets y fr. The time etension is done nlogously to the Time PBC etension in [7]. Trnsitions get n dditionl inscription of n intervl in the nturl numers. This intervl restricts the ility of the trnsition to re ccording to [8], i.e. the lower (upper) ound denes the erliest (ltest) ring time of ech trnsition. To preserve the properties of M-nets with respect to unfolding into low level nets for TM-nets, ring times re not unique to trnsition, ut ech ring mode (i.e. inding enling the trnsition) counts time steps on its own, fter the mode is enled. As such, ech trnsition my hve lrge numer of clocks showing dierent times. The current implementtion in PEP covers just n elementry version of TM-nets. We restrict the intervl ounds to nturl numers (plus innity for the upper ound). This is in contrst to the originl denition where ritrry epressions re llowed, which still hve to evlute to nturl numers ccording to the chosen inding, though. As such, the restriction is not just syntcticlly, ut the epressiveness of the simple clss is still lrge enough for mny rel world systems. 3 Tie opertor The tie opertor ws introduced to M-net lger to llow synchronous communictions [6] in compositionl wy. This etension to M-Net lger llowed to give complete semntics of B(P N) 23 [?] in terms of M-net, nd simpler semntics for FIFO uers [0, ]. To use synchronous communictions with M-nets, they re etended y new trnsition lels, clled link lels. These lels indicte tht trnsition cn eport nd/or import informtion from n synchronous chnnel. We consider set B of tie symols such tht ech 2 B hs type type(). An synchronous link d (~), where 2 B, d 2 f+;?g nd ~ 2 type(), represents 3 Bsic Petri Net Progrmming Nottion

3 n synchronous communiction ction on (the chnnel represented y). The direction of the communiction (eport or import) is given y d, nd ~ is set of rguments representing possile informtion communicted on. A link lel is multi-set of synchronous links. An emple drwn with the high-level net editor of the PEP tool is given in Fig.. On the left hnd, we show net N with synchronous nnottions. The lel f+()g on trnsition T mens tht this trnsition cn eport 2 type() on chnnel, nd f-(),+()g on T2 mens tht T2 epects to import token lelled "" nd to eport it gin vi. The result of N tie is given on the right hnd of the gure: The synchronous links of N contining were mde eective y the opertion, i.e. the trnsitions contining these synchronous links now eport nd/or import the descried informtions when they re red, ccording to the directions given y the previous nottion. Every echnged informtion goes through the creted uer plce of (nmed P6) with type() s type. Note tht pplying tie deletes the link lels concerning (not the other links) from every trnsition. P3 {} P3 {} P {,2} some_ction() (),+() T2 P {,2} some_ction() T2 T n_ction +() P4 {} n_ction T P6 {,2} P4 {} P2 {dot} (),d+(2) T3 P2 {dot} d+(2) T3 N P5 {} N tie P5 {} Fig.. An emple of using tie with the high-level editor. On the left hnd: High-level net N contining link lels, on the right hnd: the sme net fter pplying tie In the high-level editor, declrtions (respectively, deletion, modiction) of synchronous links nmes nd their corresponding types re mde through the window of the tie opertor (cf. Fig. 2). The synt for link types is the sme s for plce types. Link lels on trnsitions re dded the sme wy s ction multisets. After pplying the opertor once to some link, this one is tken ccount s rnd new link nd my e reused fterwrds to dd new nnottions on link lels nd to pply tie gin. This would then crete new uer plce for ech time the opertion is clled.

4 Fig. 2. The window of the tie opertor The tie opertor ws lso dened for PBC (see [6] for detils). This is not completely implemented yet, ut fter pplying tie to ech link, net does not contin synchronous nottions nymore, so there is wy to unfold nd nlyse it right wy. 4 Emple of n ARQ protocol We chose s n emple for the presenttion of the newly introduced fetures modelistion of n ARQ protocol. There is sender nd receiver side, where the sender communictes dt pckets to the receiver, who my nswer with positive or negtive cknowledgements. Both prts cn e found in Fig. 3, with the sender t top nd the receiver t ottom. Communiction is done in oth directions vi uered chnnel with some dely, i.e. synchronous. Moreover the cknowledgements my e deferred, such tht not every pcket will e cknowledged, ut positive cknowledgement includes ll witing ck's in etween. There is no uering of correctly received dt, so negtive cknowledgements lso cler everything ckwrds up to the negtively cknowledged pcket. If the sender receives negtive cknowledgement, it sets the net pcket pointer to the received numer, such tht the net pcket send will e the requested one. Positively cknowledged pckets just increse the counter, with some snity check done t reception. Sending dt just incorportes the pcket numer, i.e. dt content is strcted wy. At the receiver side, things re even esier nd more simplied. The received pckets re stored in the respective counter plce, which serves s source for generting (positive or negtive) cknowledgements. To model the removl of destroyed pckets y some negtive cknowledge, the received pcket counter is reset ccordingly. Thus, these pckets will not e used either y the send ck trnsition, preventing flse cknowledgements.

5 recv ck C?(0,) [;5] lst ck 3 {0..3} send dt C2!() [;3] 0 net dt {0..3} recv nk C?(,) [;5] ck chn out ^C?(,) nr (n),nr+(m),d (,,n,),d+(0,0,n,0) dt chn in ^C2!() ns (n),ns+(m),d (0,n,0),d+(,n,) ck chn in ^C!(,) ns (n),ns+(m),d (0,0,n,0),d+(,,n,) dt chn out ^C2?() nr (n),nr+(m),d (,n,),d+(0,n,0) send ck C!(0,y) recv lst recv pcket C2?() [;4] send nk [;5] y C!(,y) 0 {0..3} y [;3] 0 {0..3} lst send ck Fig. 3. ARQ model efore synchronistion nd tie The two chnnels (C from receiver to sender nd C2 vice vers) re simpli- ed versions of the FIFO uers presented in [0, ]. Unused prts hve een deleted, the dt hndling is simplied nd the chnnel use hs een etended with timing restrictions. Figure 3 just shows four trnsitions, which will crete two seprte ring uers with FIFO semntics nd comptile interfce fter ppliction of the tie opertion. Two dditionlly needed initilistion trnsitions re not shown, s they re just needed for technicl resons. The time intervls re put to ech chnnel opertion, specifying some miniml nd miml dely needed for these ctions. The chnnel trnsitions itself do not contriute to the dely with n intervl of [0; ]. The delys hve een chosen ritrrily for this emple, resulting in dely for sending pcket etween two nd 8 time units, complete round-trip with pcket sending nd cknowledgement tkes up to 7 time units in the cse of no dt loss in etween. The worst cse scenrio will tke innitely mny time units, s we do not tke into ccount firness. 5 Conclusion nd future works We hve presented the ltest fetures of the PEP tool. This new version enles veriction of Time M-nets nd dds fcilities for modelistion of synchronous

6 links in compositionl wy. Moreover, these enhncements contriute to redility nd hndiness of the editor. M-nets provide very powerful speciction formlism. The ARQ system includes some interesting fetures, using just smll numer of net elements. The time etension presented oers comfortle high-level progrmming interfce for rel-time systems. However, the synchronous links hve not yet een integrted into every prt of the tool, which is plnned for one of the net versions. This will remove some restrictions currently imposed on the user. Time Petri nets re still not supported the sme wy like ordinry Petri nets. Most notly, timed simultor is missing. Further work will include dierent time semntics nd time support in even higher speciction concepts, like SDL. Some further investigtion of cse studies of rel-time systems, including forml veriction is plnned. References. Peter Amthor, Hns Fleischhck, nd Josef Tpken. MOBY - More thn tool for the veriction of SDL-specictions. Technicl report, Fchereich Informtik, Crl von Ossietzky Universitt Oldenurg, E. Best, W. Frczk, R. P. Hopkins, H. Kludel nd E. Pelz. M-nets: n lger of high level Petri nets, with n ppliction to the semntics of concurrent progrmming lnguges. Act Informtic, 35. Springer, Hns Fleischhck nd Christin Stehno. Computing Finite Pre of Time Petri Net. In ICATPN, To pper. 4. Hns Fleischhck nd Josef Tpken. An M-net semntics for rel-time etension of SDL. In John Fitzgerld, Cli B. Jones, nd Peter Lucs, editors, FME'97: Industril Applictions nd Strengthened Foundtions of Forml Methods (Proc. 4th Intl. Symposium of Forml Methods Europe, Grz, Austri, Septemer 997), volume 33, pges 62{8. Springer-Verlg, B. Grhlmnn. The PEP Tool. Computer Aided Veriction, LNCS 254. Springer, H. Kludel nd F. Pommereu. Asynchronous links in the PBC nd M-nets. ASIAN'99, LNCS 742. Springer, Mciej Koutny. A Compositionl Model of Time Petri Nets. In M. Nielsen nd D. Simpson, editors, Appliction nd Theory of Petri Nets 2000, volume 825 of LNCS, pges 303{322. Springer-Verlg, P. Merlin nd D. Frer. Recoverility of Communiction Protocols { Impliction of Theoreticl Study. IEEE Trnsctions on Softwre Communictions, 24:036{ 043, The PEP tool F. Pommereu. FIFO uers in tie suce. DAPSYS'00. Kluwer Acdemic Pulishers, Frnck Pommereu nd Christin Stehno. Fifo uers in hot tie suce. Technicl Report , LACL, Universite Pris 2, 6 venue du generl de Gulle, 9400 Creteil, Frnce, Christin Stehno. Rel-Time Systems Design with PEP. In Joost-Pieter Ktoen nd Perdit Stevens, editors, TACAS, volume 2280 of Lecture Notes in Computer Science, pges 476{480. Springer-Verlg, 2002.