Embedded Systems CS - ES

Transcription

1 Embedded Sysems - -

2 REVIEW Peri Nes - 2 -

3 Comuing changes of markings REVIEW Firing ransiions generae new markings on each of he laces according o he following rules: When a ransiion fires from a marking M, w(, ) okens are deleed from he incoming laces of (i.e. from laces ), and w(, ) okens are added o he ougoing laces of (i.e. o laces ), and a new marking M' is roduced - 3 -

4 Acivaed ransiions Transiion is acivaed iff REVIEW Acivaed ransiions can ake lace or fire, bu don have o. The order in which acivaed ransiions fire is no fixed (i is non-deerminisic)

5 Boundedness REVIEW A lace is called k-safe or k-bounded if i conains in he iniial marking m and in all oher reachable from here markings a mos k okens. A ne is bounded if each lace is bounded. Boundedness: he number of okens in any lace canno grow indefiniely Alicaion: laces reresen buffers and regisers (check here is no overflow) A Peri ne is inherenly bounded if and only if all is reachabiliy grahs (i.e. reachabiliy grahs wih all ossible saring saes) all have a finie number of saes

6 Liveness REVIEW A ransiion T is live if in any marking here exiss a firing sequence such ha T becomes enabled An enire ne is live if all is ransiions are live Imoran for checking deadlock Live? NO YES - 6 -

7 Liveness (more recisely) A ransiion is dead a M if no marking M is reachable from M such ha can fire in M. A ransiion is live a M if here is no marking M reachable from M where is dead. A marking is live if all ransiions are live. A P/T ne is live if he iniial marking is live. Observaions: A live ne is deadlock-free. No ransiion is live if he ne is no deadlock-free

8 Deadlock REVIEW A dead marking (deadlock) is a marking where no ransiion can fire. A Peri ne is deadlock-free if no dead marking is reachable

9 - 9 - Shorhand for changes of markings )if, ( ), ( \ )if, ( \ )if, ( ) ( W W W W Le P: M () = M()+ () Firing ransiion: +: vecor add M = M+ REVIEW

10 - - Marix N describing all changes of markings Def.: Marix N (incidence marix )of ne N is a maing N: P T Z (inegers) such ha T: N(,)=() Comonen in column and row indicaes he change of he marking of lace if ransiion akes lace. )if, ( ), ( \ )if, ( \ )if, ( ) ( W W W W REVIEW

11 Incidence marix REVIEW incidence marix N of a ure (no elemenary loos) lace/ransiion-ne: N W (, ), arc from o, : W (, ), arc from o, oherwise X Conribuion of on - -

12 - 2 - Examle: N = s REVIEW

13 Sae equaion REVIEW - 3 -

14 Sae equaion REVIEW reachabiliy grah - 4 -

15 Comuaion of Invarians REVIEW We are ineresed in subses R of laces whose number of labels remain invarian under fireing of ransiions: e.g. he number of rains commuing beween Amserdam and Paris (Cologne and Paris) remains consan Imoran for correcness roofs - 5 -

16 Place - invarians REVIEW Sandardized echnique for roving roeries of sysem models For any ransiion j T we are looking for ses R P of laces for which he accumulaed marking is consan: Examle: R j ( ) j - 6 -

17 - 7 - Characerisic Vecor R R c R if if ) ( Le: ) ( ) ( ) ( c c R P j R j R j ) ( R j Scalar roduc REVIEW

18 - 8 - Condiion for lace invarians Accumulaed marking consan for all ransiions if R n R c c Equivalen o N T c R = where N T is he ransosed of N ) ( ) ( ) ( c c R P j R j R j REVIEW

19 - 9 - More deailed view of comuaions Sysem of linear equaions. Soluion vecors mus consis of zeros and ones. Differen echniques for solving equaion sysem (Gauss eliminaion, ools e.g. Malab, ) ) (... ) ( ) ( ) ( )... (... ) ( )... ( ) ( )... ( n R R R n m m n n c c c REVIEW

20 Alicaion o Thalys examle REVIEW N T c R =, wih N T = c R, - 2 -

21 Soluion vecors for Thalys examle REVIEW c R, c R, 2 c R, 3 C R,4 C R,3 C R, cr, 4 s We roved ha: he number of rains serving Amserdam, Cologne and Paris remains consan. he number of rain drivers remains consan. C R,2-2 -

22 Soluion vecors for Thalys examle REVIEW I follows: each lace invarian mus have a leas one label a he beginning, oherwise dead a leas hree labels are necessary in he examle C R,4 C R,3 C R, s C R,2-22 -

23 P5 REVIEW T T5 T2 P4 P P3 P2 P6 T3 T4 N T c R =, wih N T = T T2 T3 T4 T5 P P2 P3 P4 P5 P6-23 -

24 P P2 P3 P4 P5 P6 T - - T2 - - T3 - T4 - T

25 - 25 -

26 - 26 -

27 - 27 -

28 Place - invarians P5 T T5 T2 P4 P P3 P2 P6 T3 T4-28 -

29 Predicae/ransiion nes Goal: comac reresenaion of comlex sysems. Key changes: Tokens are becoming individuals; Transiions enabled if funcions a incoming edges rue; Individuals generaed by firing ransiions defined hrough funcions Changes can be exlained by folding and unfolding C/E nes

30 Examle: Dining hilosohers roblem n> hilosohers siing a a round able; n forks, n laes wih saghei; hilosohers eiher hinking or eaing saghei (using lef and righ fork). How o model conflic for forks? 2 forks needed! How o guaranee avoiding sarvaion? - 3 -

31 Condiion/even ne model of he dining hilosohers roblem Le x {..3} x : x is hinking e x : x is eaing f x : fork x is available Model quie clumsy. Difficul o exend o more hilosohers

32 Predicae/ransiion model of he dining hilosohers roblem () Le x be one of he hilosohers, le l(x) be he lef soon of x, le r(x) be he righ soon of x. 2 3 Tokens individuals Edges can be labeled wih variables and funcions f f 2 f

33 Predicae/ransiion model of he dining hilosohers roblem () 2 2 f f 3 f 2 f

34 Predicae/ransiion model of he dining hilosohers roblem (2) f f 2 f 3 f 4 Model can be exended o arbirary numbers of eole. No change of he srucure

35 Time and Peri Nes e.g.: Peri nes ell us ha ""a new reques can be issued only afer he resource is released Nohing abou ime In lieraure, ime has been added o PNs in many differen ways (noion of emoral consrains for: ransiions, laces, arcs) TPN

36 Timed Peri Nes TPN Each ransiion is defined recisely based on conneciviy and okens needed for ransiion Given an iniial condiion, he exac sysem sae a an arbirary fuure ime T can be deermined Timed Peri Nes becomes a 7-ule sysem PN = (P,T,F,W,K, M, ) = {, 2, n } is a finie se of deerminisic ime delays o corresonding i

37 Time and Peri Nes (TPN) adding (quaniaive) ime o PNs is o inroduce emoral consrains on is elemens: e.g., a ransiion mus fire afer 5 msec moving Drill u 5 msec 2 msec Drill down Drill down 5 msec 2 msec 9 msec Drill u 7 msec 4 msec 2msec

38 Producion sysem - To level eri ne

39 magazine/deo NC axis o level grier drilling machine

40 magazine/deo - 4 -

41 NC axis - 4 -

42 - 42 -

43 Evaluaion Pros: Aroriae for disribued alicaions, Well-known heory for formally roving roeries, Cons : PN roblems wih modeling iming (exensions in TPN) no rogramming elemens, no hierarchy (exensions available) Exensions: Enormous amouns of effors on removing limiaions. Remark: A FSM can be reresened by a subclass of Peri nes, where each ransiion has exacly one incoming edge and one ougoing edge

44 Summary Peri nes: focus on causal deendencies Condiion/even nes Single oken er lace Place/ransiion nes Mulile okens er lace Predicae/ransiion nes Tokens become individuals Dining hilosohers used as an examle Exensions required o ge around limiaions

45 SDL - Secificaion and Descriion Language

46 SDL - Secificaion and Descriion Language Used here as a (rominen) examle of a model of comuaion based on asynchronous message assing communicaion. aroriae also for disribued sysems Language designed for secificaion of disribued sysems. Daes back o early 7s, Formal semanics defined in he lae 8s, Defined by ITU (Inernaional Telecommunicaion Union): Z. recommendaion in 98 Udaes in 984, 988, 992, 996 and 999 Anoher acronym SDL ( Sysem Design Languages )

47 SDL - Secificaion and Descriion Language Provides exual (ool rocessing) and grahical formas (user ineracion) Abiliy o be used as a wide secrum language from requiremens o imlemenaion Jus like SaeChars, i is based on he CFSM (Communicaing FSM) model of comuaion; each FSM is called a rocess. Wih SDL he roocol behaviour is comleely secified by communicaing FSM. The formal basis of SDL enables he use of code generaion ool chains, which allows an auomaed imlemenaion of he secificaion

48 SDL - Secificaion and Descriion Language However, i uses message assing insead of shared memory for communicaions SDL suors oeraions on daa objec oriened descriion of comonens

49 Srucuring SDL designs SDL sysems can be srucured in various means: A sysem consiss of a number of blocks conneced by channels, each block may conain a subsrucure of blocks or i may conain rocess ses conneced by signals. Processes execue concurrenly wih oher rocesses and communicae by exchanging signals; or by remoe rocedure calls

50 Secifying behaviour. The behaviour of a rocess is described as an exended FSM: When sared, a rocess execues is sar ransiion and eners he firs sae. (riggered by signals) 2. In ransiions, a rocess may execue acions. 3. E.g.: Acions can assign values o variable aribues of a rocess, branch on values of exression, call rocedures, creae new rocesses, send signal o oher rocesses

51 SDL-reresenaion of FSMs/rocesses sae inu ouu - 5 -

52 Communicaion among SDL-FSMs Communicaion beween FSMs (or rocesses ) is based on message-assing, assuming a oenially indefiniely large FIFO-queue. Each rocess feches nex enry from FIFO, checks if inu enables ransiion, if yes: ransiion akes lace, if no: inu is ignored (exceion: SAVEmechanism)

53 Deerminae? Le okens be arriving a FIFO a he same ime: Order in which hey are sored, is unknown: All orders are legal: simulaors can show differen behaviors for he same inu, all of which are correc

54 Oeraions on daa Variables can be declared locally for rocesses. Their ye can be redefined or defined in SDL iself. SDL suors absrac daa yes (ADTs). Examles:

55 Process ineracion diagrams Ineracion beween rocesses can be described in rocess ineracion diagrams (secial case of block diagrams). In addiion o rocesses, hese diagrams conain channels and declaraions of local signals. Examle:, B

56 Designaion of reciiens. Through rocess idenifiers: Examle: OFFSPRING reresens idenifiers of rocesses generaed dynamically. 2. Exlicily: By including he channel name. 3. Imlicily: If signal names imly channel names (B Sw) Couner TO OFFSPRING Couner Via Sw

57 Hierarchy in SDL Process ineracion diagrams can be included in blocks. The roo block is called sysem. Processes canno conain oher rocesses, unlike in SaeChars

58 Hierarchy of a SDL secificaion

59 Timers Timers can be declared locally. Elased imers u signal ino queue (no necessarily rocessed immediaely). RESET removes imer (also from FIFO-queue)

60 SDL alicaion The semanics of SDL defines he sae sace of he secificaion. This sae sace can be used for various analyses and ransformaion echniques, e.g.: sae sace exloraion, simulaion checking he SDL-secificaion for deadlocks/lifelocks deriving es cases auomaically code generaion for an execuable rooye or end sysem - 6 -

61 Summary MoC: finie sae machine comonens + non-blocking message assing communicaion Reresenaion of rocesses Communicaion & block diagrams Timers and oher language elemens Excellen for disribued alicaions (e.g., Inegraed Services Digial Nework (ISDN)) Commercial ools available from SINTEF, Telelogic, Cinderella (//