Business Process Management

Transcription

1 Business Process Management Theory: The Pi-Calculus Frank Puhlmann Business Process Technology Group Hasso Plattner Institut Potsdam, Germany 1

2 What happens here? We discuss the application of a general theory for the description of mobile systems into the area of BPM and its wider parts 2

3 What are mobile systems? Mobile systems are made of entities that move in a certain space Different kinds of mobility: 1. Links that move in an abstract space of linked processes 2. Processes that move in an abstract space of linked processes 3

4 Dynamic Topologies Mobile systems describe behavior with dynamic topologies, i.e. changing structures This is contrary to static structures for the description of behavior, i.e. Petri nets: 4

5 S S B S S S C S Link Passing Mobility 5

6 Outline Pi-Calculus Part Motivation The Theory of the Pi-Calculus Workflow and Data Patterns Application of the Pi-Calculus to BPM Verification 6

7 Motivation The Shifting Focus 7

8 A Shift in Theoretical Foundations From: Sequential systems Lambda-Calculus (Church, Kleene, 1930) Over: Parallel systems Petri nets (Petri, 1960) To: Mobile systems Pi-Calculus (Milner, Parrow, Walker 1990) 8

9 The Lambda-Calculus Defined to investigate the definition of functions which are used for sequential computing Precise definition of a computable function Recursion Algebra: Compositional Structure Smallest universal programming language 9

10 Start Task Decision Stop Sequential System 10

11 Petri nets Business processes require parallelism Split, Joins Dependencies Petri nets build a foundation for BPM Explicit states and structure Strong visualization 11

12 Parallel System 12

13 Petri net drawbacks Good and Bad: Static structure No advanced composition Regarding behavioral workflow patterns: Excellent support for basic tasks Poor support for advanced tasks 13

14 The Pi-Calculus Describes mobile systems Agents (processes) interacting by Names with agile scopes Is an algebra 14

15 P3 P3 P2 P4 P2 P4 Evolution P5 P5 P1 P1 Mobile System 15

16 The Pi-Calculus Advantage Overcomes the limitations of static structures Has the pros and cons of an algebra Supports all behavioral workflow patterns 16

17 Why mobile systems? What s wrong with BPM and Petri nets? Why do we need mobile instead of parallel systems? Strong discussion between academics and practitioners 17

18 Why mobile systems? We argue: Three major shifts in BPM will lead to mobile systems as a theoretical foundation 18

19 BPM Shift 1: From Static to Dynamic Systems Traditional: Static, state-based systems e.g. Workflow nets, Activity Diagrams, BPMN (Token-Place concept) Today: Inter-organizational business processes Hard to change 19

20 Receive and Process Answer Start Send Request Finish Timeout Sample Process 20

21 Receive Request Send Response Corresponding Process 21

22 Receive Request Send Response Requests Responses System Border Receive and Process Answer Start Send Request Finish Timeout Static Interaction 22

23 Dynamic Systems No explicit state description Each task is mapped to a service: Each task has pre- and postconditions (i.e. in- and outgoing messages) All tasks are swimming inside a serviceoriented environment 23

24 Service Repository Find Publish Service Requester Bind Service Provider Service-oriented Architecture 24

25 Reason 1: Mobile systems are based on the idea of interaction by messages/events instead of state transitions Support for dynamic binding 25

26 BPM Shift II: From Central Engines to Distributed Services Follows direct from the last shift: No more centralized engine as for intraorganizational workflow Instead distributed services of different granularity 26

27 Other space S2 Send Response Our space P2 S1 Receive Request P1 Send Request Receive and Process Answer P3 Timeout Distributed Services 27

28 Reason II: Mobile systems support advanced composition and visibility of their parts Support distribution and the serviceoriented idea for BPM 28

29 BPM Shift III: From Closed to Open Environments The environment where processes are executed is shifting strongly from closed to open, which means: Less accessibility More uncertainty Constant change regardless of us Number of possible interaction partners rises fast 29

30 Issues regarding Open Environments Constant change requires dynamic adaption Flexible discovery and integration More agile interaction 30

31 Reasons III: Mobile systems describe dynamic process structures Based on a prototypical viewpoint Support flexibility regarding discovery and interaction for BPM 31

32 Motivation in a Nutshell Mobile systems support advanced key concepts of BPM: Dynamic Binding Composition and Visibility Change The Pi-Calculus is a process algebra for mobile systems 32

33 The Theory of the Pi- Calculus Syntax & Semantics 33

34 Informal Introduction The Pi-Calculus is based on few concepts: Agents (Processes) Names Synchronized Interactions 34

35 talk TIM TOM TIM def = talk message.0 TOM def = talk(message).τ TOM.0 SYSTEM def = TIM TOM Basic Interaction 35

36 talk talk TIM TOM TIM TOM print Evolution print PRINTER PRINTER TIM def = talk print.0 TOM def = talk(print).print file.0 PRINTER def =!print(file).τ PRINT.0 SYSTEM def = TIM TOM PRINTER Advanced Interaction 36

37 TIM talk TOM talk TIL TOM TIL TIM def = talk TOM message.0 + talk TIL message.0 TIM def = [x = ]talk TOM message.0+ [x = ]talk TIL message.0 Choice 37

38 TIM talk TOM talk TIL TOM TIL TIM def = talk TOM message.0 talk TIL message.0 Concurrency 38

39 GENERATOR GENERATOR def = (νx)get x.0 Name Creation 39

40 The Pi-Calculus BNF P ::= M P P νz P!P M ::= 0 π.p M + M π ::= x y x(z) τ [x = y]π 40

41 Abbreviations 3 Composition: (P ) = P P P Summation: with index: 1 3 (P ) = P + P + P 1 3 (d i.0) = d d d 3 0 i=1 Sequence:{π} 3 1 = π.π.π 41

42 Bound and free names In each of x(z).p and νz P the displayed occurrence of z is binding with scope P An occurrence of a name in an agent is bound if it is, or it lies within the scope of, a binding occurrence of the name An occurrence of a name in an agent is free if it is not bound 42

43 Substitution We write P { y 1 / x1,, y n / xn } for the simultaneous substitution of yi for all free occurrences of xi in P, with the change of bound names if necessary to prevent any of the new names yi from becoming bound in P 43

44 Defined Agent Identifiers A defined agent identifier is given by: A(x 1,, x n ) def = P Then A(y 1,, y n ) behaves as P { y 1 /,, y n / } x1 xn if x i are free names in P the definition can be thought of as an agent declaration with x1,..., xn as formal parameters, and the identifier A(y1,..., yn) as an invocation with actual parameters y1,..., yn 44

45 A b B A' b B' x C Evolution C x A B b x.a b(y).b b x.a b(y).b C A B { x / y } C Example: Communication 45

46 A b B scope of x A' b B' scope of x x x Evolution x x' C D C D b x.a C (νx)(b(z).b D) A C (νx )(B { x / x }{ x / z } D{ x / x }) Example: Scope Intrusion 46

47 scope of x A b B A' b B' scope of x x C Evolution x C (νx)(b x.a C) b(z).b (νx)(a C B { x / z }) Example: Scope Extrusion 47

48 A def = b x.a + A M(x) def = write(x).m(x) + read x.m(x) (νwrite, read)(m(z) A) Example: Recursion 48

49 The Polyadic Pi- Calculus How can we send messages consisting of multiple names? 49

50 Syntactical enhancement: Sequences: x 1,..., x n x Empty messages: The Polyadic Pi-Calculus x y 1,..., y n.p (νw)(x w.w y w y n.p ) x(z 1,..., z n ).P x(w).w(z 1 ).....w(z n ).P x ỹ x iff ỹ =, x( z) x iff z = 50

51 Reduction Evolution is formally defined as reduction The essence of reduction is captured in two axioms: (x y.p 1 + M 1 ) (x(z).p 2 + M 2 ) P 1 P 2 { y / z } τ.p + M P and three rules: from P 1 P 1 infer P 1 P 2 P 1 P 2 from P P infer νz P νz P from P P and P Q and P Q infer Q Q 51

52 Structural Congruence The axioms of structural congruence (Part 1): SC-MAT: [x = x]π.p π.p SC-SUM-ASSOC: SC-SUM-COMM: SC-SUM-INACT: SC-COMP-ASSOC: SC-COMP-COMM: SC-COMP-INACT: M 1 + (M 2 + M 3 ) (M 1 + M 2 ) + M 3 M 1 + M 2 M 2 + M 1 M + 0 M P 1 (P 2 P 3 ) (P 1 P 2 ) P 3 P 1 P 2 P 2 P 1 P 0 P 52

53 Structural Congruence The axioms of structural congruence (Part 2): SC-RES: SC-RES-INACT: SC-RES-COMP: SC-REP UNFOLDING: νzνw P νwνz P νz 0 0 νz (P 1 P 2 ) P 1 νz P 2, if z fn(p 1 )!P P!P A(ỹ) P {ỹ/ x } if A( x) def = P 53

54 A def = (νz)a(x, y).x z.y.0 B def = a c, b.b.0 C def = c(m).0 P def = A B C Example: Reduction 54