1. Rigoros and Adaptive... Information Systems1 Development of Rigorous Adaptive Information Systems Dr. Nasreddine Aoumeur FIN, ITI, DB group aoumeur@iti.cs.uni-magdeburg.de Course Site: wwwiti.cs.uni-magdeburg.de/~aoumeur wwwiti.cs.uni-magdeburg.de/iti_db/lehre/oois/inde

2. Rigoros and Adaptive... Information Systems2 Information Systems: Working definition – reactive systems (i.e. in continuous interaction with their environment), with –large amount of immutable and non- immutable data (i.e. fixed and changing) and, with – processes and activities for exhibiting behaviors on these (state-less and –full) data.

3. Rigoros and Adaptive... Information Systems3 Different generations of CMs : “Entity first” State-less and -ful DATA Processes and Rules IS Conceptual Model Entity-Relationship[1973..] - Intuitive / Simple - Revolutionary for IS - UoD : Entities+Relations - Mathematically sound - Rich abstraction mechnanisms - Different variants (NIAM / SADT / MERISE /..) Process-centric Formalisms - CCS, CSP, DFD, Petri Nets,.. - Synchronous / asynchronous - Mathematically sound - Executable / operational

4. Rigoros and Adaptive... Information Systems4 Different generations of CMs : “Object first” State-less and -ful DATA Processes and Rules IS Conceptual Model Object Paradigm[1980..] - Really Intuitive / highly accepted - Object (Id, structure / dynamic) - UoD : Interacting objects community - Rich abstraction mechnanisms (e.g. Class, inheritance, role, aggregation,..) - Different formal interpretations Behavior-centric OO Formalisms - OO Petri Nets, Mondel, JSD.. - Mathematically sound - Executable / operational / concurrent - Cope with data and process around objects

5. Rigoros and Adaptive... Information Systems5 Current generation of CMs : “Interaction first” Aspect-/connector-/meta-level All What is : - Evolving ( business rules, market laws, cross-organizational policies, …) - Cross-Cutting (security, management,..) - Non-functional (availability, performance,..) Stable and invariant entities IS Conceptual Model Aspect/archietctural Paradigm - Explicit separation between Coordination and computation - Separation between what is evolving from what is stable - Dynamic shifting-down / up of changing behavior - Suitable for services and mobility Entity Interfaces Dynamically weaving

6. Rigoros and Adaptive... Information Systems6 First generation of CMs : “Entity first” Processes and Rules E/R Conceptual Model Entity Name Attribute1 : Type1 Attribute2 : Type2.... Attributei : Typei Property1..... n-m i-j Assoc PART IS-A m Entit(ies) n Entit(ies)

7. Rigoros and Adaptive... Information Systems7 First generation of CMs : “Entity first” E/R Conceptual Model Customer Name : String Birth-Date : Date Address : Address Income : Money Open-Date Bank 1-2 0-N Own (Running) Account Number : Nat Balance : Money Limit : Money History : List[Date,Money] IS-A Saving Account Number : Nat Interest : Percent Balance Processes and Rules Account USE : First open --- then deposit – then (withdraw-deposit)* - then Close-or-be-closed

8. Rigoros and Adaptive... Information Systems8 First generation of CMs : “Entity first” E/R Conceptual Model Customer Name : String Amount Date 1-2 0-N Withdraw AutomaticTellerMachine ATM-Reference : String Cash : Hidden Bank : String Transaction : List[Money] History :List[Card-Nb,Acnt-Nb,Money Bank-Card Number : Nat Account-Nb: Nat Code : String Processes and Rules ATM-use : First enter-card – then enter-code – then enter-transaction—get money

9. Rigoros and Adaptive... Information Systems9 First generation of CMs : “Entity first” E/R Conceptual Model Student Name : String Subscription-Nb Semester Date-Out Date-Back 0-N 0-3 Borrow Book Reference : String Name : String Author : String Publisher : String Processes and Rules First subscribe-- Get library-card – (Borrow – Return –or– Penality)*--(be)Unsubscribe(d)

10. Rigoros and Adaptive... Information Systems10 First CM generation : Process With Petri Nets What is a behavioral process in IS--- at the highest-abstract-level? States (instances) : In terms of (un-)availability. That a state instance is regarded as a resource -Example : An account (instance) is a resource, a book (instance) is a resource. (State-based) Actions: The allowed ordering causality between states (instances) via actions (i.e. operations, methods). -Example : First open-account, then deposit then looping withdraw-depsit-then close

11. Rigoros and Adaptive... Information Systems11 Author : Carl-Adam Petri Live currently in Hamburg (honorary Professor at the Univ.) History: Model introduced by C.A. Petri in 1962 – (Physics) Ph.D. Thesis: “Communication with Automata” PNs Applications: Distributed computing, manufacturing, control, information systems, communication networks, transportation… Purpose: PNs specify / validate / verify explicitly and graphically: –sequencing/causality actions on states –conflict/non-deterministic choice actions –True concurrency actions on states First CM generation : Process With Petri Nets

12. Rigoros and Adaptive... Information Systems12 (Introductory) Reference: Tadao Murata. “Petri nets: Properties, Analysis and Applications.” Proc. of the IEEE, 77(4), 1989. Wolfgang Reisig, “Petri Nets”, Springer, EATCS Monographs on Theoretical Computer Science, 1985 (Also in German). First CM generation : Process With Petri Nets

13. Rigoros and Adaptive... Information Systems13 First CM generation : Process With Petri Nets Conceptual philosophy under Petri nets: 1.In any system, we have resources -Artifact-based resources : data, objects, events, -Real resources : printers, buffers, CPUs 2.There is generally, a number of available instances for each kind of resource in the system. 3.Actions (behavior, dynamics) in the system allows: -consuming (using) some resources and -producing new ones or updating existing ones (under some conditions).

14. Rigoros and Adaptive... Information Systems14 With each kind of ressource is described by: – a PLACE graphically as circle is associated Ressource instances are included as: – BLACK DOTS (called TOKENS ) within the corresponding ressource kind place. Actions called TRANSITIONS are: – graphically represented as a BOX or RECTANGLE. Ressources consumption are captured by: – INPUT ARCS- --valuted or inscribed by the numbers of required ressouces--- From the corresponding ressource place to the associated action box. Ressources production or changes are captured by: – OUTPUT ARCS---valuted or inscribed by the numbers of produced ressouces--- From the associated action box to the corresponding target resource place PETRI NETS ARE BIPARTITE GRAPHS First CM generation : Petri Nets Concepts

15. Rigoros and Adaptive... Information Systems15 First CM generation : Petri Nets Concepts 2 4 30 P1 P2 T1 INPUT place with five (5) tokens as Marking INPUT place with five (5) tokens as Marking INPUT arc with two (2) (required tokens) as arc-inscription INPUT arc with two (2) (required tokens) as arc-inscription Transition named T1 OUTPUT arc with Four (4) (produced tokens) as arc-inscription OUTPUT arc with Four (4) (produced tokens) as arc-inscription OUTPUT place with thirty (30) tokens as marking OUTPUT place with thirty (30) tokens as marking

16. Rigoros and Adaptive... Information Systems16 First CM generation : Petri Nets Illustrations BankOK ToOpen OpenAcnt Deposit Opened AcntState Withdraw Deposit Transfert Closed

17. Rigoros and Adaptive... Information Systems17 First CM generation : Petri Nets Illustrations 1 1 30 Books@Library ToBorrow Borow 1 Borrowed-Books ToReturn ReturnReturn&Penalty Penality2Pay 6 Card

18. Rigoros and Adaptive... Information Systems18 First CM generation : Petri Nets Strenghts and choice

19. Rigoros and Adaptive... Information Systems19 First CM generation : Petri Nets Strenghts

20. Rigoros and Adaptive... Information Systems20 t2 t3 t1t4 First CM generation : Petri Nets Internals concurrency

21. Rigoros and Adaptive... Information Systems21 t2 t3 t1t4 concurrency First CM generation : Petri Nets Internals

22. Rigoros and Adaptive... Information Systems22 Modeling synchronization control writing k reading k k k

23. Rigoros and Adaptive... Information Systems23 First CM generation : Petri Nets Typical Use ToSend Send msg Receive Ack Send Ack Receive msg T oReceive CommunicationProtocols

24. Rigoros and Adaptive... Information Systems24 First CM generation : Petri Nets Typical Use Operating Systems Produce Consume Buffer

25. Rigoros and Adaptive... Information Systems25 First CM generation : Petri Nets Typical Use Embedded Systems Coins Change GetCigaretteGetCaffe Machine-I tems GetWater 2$4$ 3$ 75P 25P WaterCigarette Caffe

26. Rigoros and Adaptive... Information Systems26 First CM generation: Petri Nets Formalisms A Petri nets in a five tuples PN = (P, T, W, M0) –P = {p1,p2,....,pn} is a finite sets of places (circles) –T = {t1, t2,...,tq} is a finite set of transitions (boxes) –F  (P x T)  (T X P) is a finite set of arcs. An input (resp. output) ) arc joins a place to transition (resp. transition to place). NEVER PLACE TO PLACE or TRANSITION TO TRANSITION. –W : F  {1,2,...} is a weight function attached to the arcs. If the weight in missing it is implicitly one. –M0 : P  {0,1,2,....} is the intial marking. M0(p), p  P is the marking (i.e. numbers of tokens) of the place p.

27. Rigoros and Adaptive... Information Systems27 First CM generation: Petri Nets Formalisms Notations : –  t : the set of input places of transition t. that is the set of places p such that (p,t)  F. – t  : the set of output places of transition t. That is, p such that (t,p)  F. –  p : the set of input transitions of place p. that is the set of transitions such that (t,p)  F. – p  : the set of output places of transition t. That is, t such that (p,t)  F.

28. Rigoros and Adaptive... Information Systems28 Dynamics of Petri nets : –A transtion t is said to be enabled if, whatever p   t, p contains a number of tokens greater of equal than W(p,t) (i.e. M(p)  W(p,t)) –Firing an enabled transition t, consists in : »Removing W(p,t) tokens from each p   t »Adding W(t, p) tokens from each p  t  »That is, M‘(p) = M(p) – W(p,t) + W(t,p) – A sequence of transitions firing is generally represented by  =, and – We say that the corresponding resulting marking is: M 0 --  --M k First CM generation: Petri Nets Dyanmisms

29. Rigoros and Adaptive... Information Systems29 First CM generation : Petri Nets Dynamisms Operating Systems Animated Produce Consume Buffer

30. Rigoros and Adaptive... Information Systems30 First CM generation : Petri Nets Dynamisms Embedded Systems Animated Coins Change GetCigaretteGetCaffe Machine-I tems GetWater 5$4$ 3$ 75P 25P Water CigaretteCaffe 18 10 6 7 1 1 1 100 2 2 175

31. Rigoros and Adaptive... Information Systems31 H2H2 O2O2 H2OH2O t 2 2 First CM generation : Petri Nets Dynamisms Chimical Reactions : 2H2 + O2  2H2O

32. Rigoros and Adaptive... Information Systems32 Incidence matrix : A = [a ij ] –is an n  m matrix of integers –its typical entry is given by a ij = a ij + - a ij - –Where a ij + = w(T,P) is the weight of the arc from transition T to its output place P –and a ij - =w(P.T) is the weight of the arc from the input place P to the transition T. First CM generation : Petri Nets Internals

33. Rigoros and Adaptive... Information Systems33 Given an initial marking M 0, let  be a firiable sequence of transitions which applies to M 0. The counting vector V  of is the vector V  = [v1,v2,..,vj,...vq] is the numbers of times tj is included in . If M is the marking obtained by firing , then: » M t = M 0 t + AV  t. With t denotes the transpose. First CM generation : Petri Nets Internals

34. Rigoros and Adaptive... Information Systems34 Illustration: 2 t1 p1 t2p2 t4 t3 p3 p4 4 2 2 First CM generation : Petri Nets Internals

35. Rigoros and Adaptive... Information Systems35 t1 t2 t3 t4 p1 1 -2 -1 0 A = p2 0 4 0 -1 p3 0 0 1 -1 p4 0 0 -2 2 Let M 0 = [3,0,0,2] and  =, that is V  = [0,1,1,1]. Then M = [0, 3, 0, 2] using the formulas. First CM generation : Petri Nets Internals

36. Rigoros and Adaptive... Information Systems36 Illustration by firing t2, t3, t4 : 2 t1 p1 t2p2 t4 t3 p3 p4 4 2 2 First CM generation : Petri Nets Internals

37. Rigoros and Adaptive... Information Systems37 Behavioral: depend on the initial marking (most interesting) – Reachability – Boundedness – Schedulability – Liveness – Conservation Structural: do not depend on the initial marking (often too restrictive) – Consistency – Structural boundedness First CM generation : Petri Nets Properties

38. Rigoros and Adaptive... Information Systems38 Marking M is reachable from marking M 0 if there exists a sequence of firings   M 0 t 1 M 1 t 2 M 2 … M that transforms M 0 to M. The reachability problem is decidable. t1p1 p2 t2 p4 t3 p3   = (1,0,1,0) M = (1,1,0,0)   = (1,0,1,0) t3 M 1 = (1,0,0,1) t2 M = (1,1,0,0) First CM generation : Petri Nets Propeties

39. Rigoros and Adaptive... Information Systems39 Liveness: from any marking any transition can become fireable – Liveness implies deadlock freedom, not viceversa Not live First CM generation : Petri Nets Propeties

40. Rigoros and Adaptive... Information Systems40 Boundedness: the number of tokens in any place cannot grow indefinitely – (1-bounded also called safe ) – Application: places represent buffers and registers (check there is no overflow) Unbounded First CM generation : Petri Nets Propeties

41. Rigoros and Adaptive... Information Systems41 Conservation: the total number of tokens in the net is constant Not conservative First CM generation : Petri Nets Propeties

42. Rigoros and Adaptive... Information Systems42 Structural analysis techniques – Incidence matrix – T- and S- Invariants State Space Analysis techniques – Coverability Tree – Reachability Graph First CM generation : Petri Nets Propeties

43. Rigoros and Adaptive... Information Systems43 Incidence Matrix Necessary condition for marking M to be reachable from initial marking M 0 : there exists firing vector v s.t.: M = M 0 + A v p1p2p3t1 t2 t3 A= -100 11-1 0-11 t1t2t3 p1 p2 p3 First CM generation : Petri Nets Propeties

44. Rigoros and Adaptive... Information Systems44 State equations p1p2p3t1 t3 A= -100 11-1 0-11 E.g. reachability of M =|0 0 1| T from M 0 = |1 0 0| T but also v 2 = | 1 1 2 | T or any v k = | 1 (k) (k+1) | T t2100+ -100 11-1 0-11 001=101 v 1 = 101 First CM generation : Petri Nets Propeties

45. Rigoros and Adaptive... Information Systems45 State equations and invariants Solutions of Ax = 0 (in M = M 0 + Ax, M = M 0 ) T-invariants – sequences of transitions that (if fireable) bring back to original marking – periodic schedule in SDF – e.g. x =| 0 1 1 | T p1p2p3t1 t3 A= -100 11-1 0-11 t2 First CM generation : Petri Nets Propeties

46. Rigoros and Adaptive... Information Systems46 Application of T-invariants Scheduling – Cyclic schedules: need to return to the initial state i *k2 + *k1 Schedule: i *k2 *k1 + o T-invariant: (1,1,1,1,1) o First CM generation : Petri Nets Propeties

47. Rigoros and Adaptive... Information Systems47 Properties that depend on the initial marking Reachability –Mn is reachable from M0 if exists a sequence of firings that transform M0 into Mn –reachability is decidable, but exponential Boundedness –a PN is bounded if the number of tokens in each place doesn’t exceed a finite number k for any marking reachable from M0 –a PN is safe if it is 1-bounded First CM generation : Petri Nets Properties

48. Rigoros and Adaptive... Information Systems48 Liveness –a PN is live if, no matter what marking has been reached, it is possible to fire any transition with an appropriate firing sequence –equivalent to deadlock-free Reversibility –a PN is reversible if, for each marking M reachable from M0, M0 is reachable from M –relaxed condition: a marking M’ is a home state if, for each marking M reachable from M0, M’ is reachable from M First CM generation : Petri Nets Properties

49. Rigoros and Adaptive... Information Systems49 Coverability –a marking is coverable if exists M’ reachable from M0 s.t. M’(p)>=M(p) for all places p Persistence –a PN is persistent if, for any two enabled transitions, the firing of one of them will not disable the other –then, once a transition is enabled, it remains enabled until it’s fired –all marked graphs are persistent –a safe persistent PN can be transformed into a marked graph First CM generation : Petri Nets Properties

50. Rigoros and Adaptive... Information Systems50 Synchronic distance –maximum difference of times two transitions are fired for any firing sequence –well defined metric for condition/event nets and marked graphs Fairness –bounded-fairness: the number of times one transition can fire while the other is not firing is bounded –unconditional(global)-fairness: every transition appears infinitely often in a firing sequence First CM generation : Petri Nets Properties

51. Rigoros and Adaptive... Information Systems51 Coverability tree –tree representation of all possible markings »root = M0 »nodes = markings reachable from M0 »arcs = transition firings –if net is unbounded, then tree is kept finite by introducing the symbol  –Properties »a PN is bounded iff  doesn’t appear in any node »a PN is safe iff only 0’s and 1’s appear in nodes »a transition is dead iff it doesn’t appear in any arc »if M is reachable form M0, then exists a node M’ that covers M First CM generation : Petri Nets Properties

52. Rigoros and Adaptive... Information Systems52 Coverability tree example t3 p2 t2 p1 t1 p3 t0 M0=(100)

53. Rigoros and Adaptive... Information Systems53 Coverability tree example t3 p2 t2 p1 t1 p3 t0 M0=(100) M1=(001) “dead end” t1

54. Rigoros and Adaptive... Information Systems54 Coverability tree example t3 p2 t2 p1 t1 p3 t0 M0=(100) M1=(001) “dead end” t1t3 M3=(10)

55. Rigoros and Adaptive... Information Systems55 Coverability tree example t3 p2 t2 p1 t1 p3 t0 M0=(100) M1=(001) “dead end” t1t3 M3=(10) t1 M4=(01)

56. Rigoros and Adaptive... Information Systems56 t3 p2 t2 p1 t1 p3 t0 M0=(100) M1=(001) “dead end” t1t3 M3=(10) t1 M4=(01) t3 M3=(10) “old” First CM generation : Petri Nets Properties

57. Rigoros and Adaptive... Information Systems57 t3 p2 t2 p1 t1 p3 t0 M0=(100) M1=(001) “dead end” t1t3 M3=(10) t1 M4=(01) t3 M6=(10) “old” t2 M5=(01) “old” First CM generation : Petri Nets Properties

58. Rigoros and Adaptive... Information Systems58 100 M0=(100) M1=(001) “dead end” t1t3 M3=(10) t1 M4=(01) t3 M6=(10) “old” t2 M5=(01) “old” t1t3 t1 1010 001 0101 t3 t2 coverability graph coverability tree First CM generation : Petri Nets Properties