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10th International Conference on
    Business Process Management
    September 3-6, 2012 | Tallinn, Estonia




Isotactics as a Foundation for
Alignment and Abstraction
of Behavioral Models

Artem Polyvyanyy*                         Matthias Weidlich                              Mathias Weske
BPM Discipline                            Faculty of Industrial                          BPT Group
Information Systems School                Engineering & Management                       Hasso Plattner Institute
Faculty of Science & Engineering          Technion                                       University of Potsdam
    Queensland University of Technology      Technion – Israel Institute of Technology        Hasso Plattner Institute
    Brisbane, Australia                      Haifa, Israel                                    Potsdam, Germany
Modeling


                                                                                          Mapping

                                                                                         Reduction

                                                                                         Pragmatics




                                                                                              [ Weidlich 2011]

Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012                           2
Process Modeling




                                                                                         [ Weidlich 2011]

Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012                      3
Motivation (Structural Abstraction)
    Abstraction is at the core of model creation, which comprises the mapping and reducing the entities
    of a problem domain for a certain purpose
    In process models, abstraction is achieved by means of sub-processes
    A sub-process in an abstract version of an original process model is a contracted to a single vertex
    connected, usually single-entry-single-exit, sub-graph of the original model

                                                                   a           In stock
                                                                                                            c                   d             e
                                                   Receive                                         Ship             Send            Receive
                                   (a)              order                                        products            bill           payment
       Mapping                                                                 Make
                                                                              products

     α = (a,{s,t})
                                                               Not in stock
                                                                                             b              Reducing
                                                       α                                 β
     β = (b,{u,v,w})                                                                                        Purchase        u
             ...                                                         Not in stock
                                                                                                              raw
                                                                                                             material                                  w
                                                                                                                                        Manufacture
                                                                                                                                         products
                                                       Order
                                                                                                              Make
                                                                                                            production
                                                                                                               plan         v
                                         s                               t
                                             Analyze           Check
                       (b)                    order            stock
                                                                                                                x                   y              z
                                                                                                      Ship               Send            Receive
                                                                                                    products              bill           payment
                                                                              In stock


 [ Artem Polyvyanyy, Sergey Smirnov, Mathias Weske: The Triconnected Abstraction of Process Models. BPM 2009: 229-244 ]

Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012                                                                     4
Beyond Structural Abstraction
    Structural abstraction defines a relation on process models with the intuitive behavioral
    relation between original models and their abstract versions
    Do other (behavioral) abstraction relations on process models exist?
    o    Which mappings are allowed?
    o    Which reductions are allowed?
    o    How behavior is preserved?
                                                          Abstraction?

                           Collect
           Select                                                                     Study
                           product
          product                                                                    product
                             info
                                           Perform                                                   Perform
                                           analysis                                                  analysis
                           Collect                                                   Collect
                           market                                                    market
                            info                                                      info




                                     (a)                  Abstraction?                         (b)


Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012                          5
Alignment w/o Restrictions
                                                                  Collect       e          δ
                                                                  product
                                                                    info
                                                         g
α
                                              Perform
                                              detailed
                           a                  analysis
                  Study
                                                                  Collect
                 product
                                                                  market
                               Perform    c                        info
(a)                                                                             f
                                initial
                               analysis
                                                                            d
                                                                                                      γ
                                                             Evaluate
                 Study
                                                             analysis
                 market
                                                              results
                           b




                                                                    Select
                                                                                    w   Collect   x
                                                                                        product
                                                                    product
                                                                                          info
α = ({a},{w,x})                               (b)                                                     Perform
                                                                                                      analysis
β = ({b,c,d},{y,z})                                                                     Collect
                                                                                                                 z
γ = ({c,d,g},{z})                                                                       market
                                                                                                  y
                               β
                                                                                         info

δ = ({e,f},{x,y})

Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012                               6
Alignment of Petri nets
                                                                                                           t10
                                                                                                 p12                   p11
                 α                                                      t13
                                                                                   p15 t12
                                                                                                          e                    t9 p    t8
                                t2                                                                                                  10
                      p2                  p3
                                                                        g                                t11
                                a                             t5                                 p14
            p1 t1                              t4 p 6                                                                                       t14 p
                                                                              p7                          f                  p13    p9           16

(a)                             t3                            c                        t6
                      p4                  p5                                                 p8                       t7
                                b                                                                         d
                                                                                                                           γ

                                δ                                                                  t10
                                                                                                               p11
                           t2             t3             t4
                 p2                            p4                  p5
                           w                            x                                   t8                   t9
       p1   t1                       p3                                     t7 p9                                          p12
(b)                                                     t6
                                                                                            z
                                                                                                                                         α = ({a},{w,x})
                 p6                       t5   p7                  p8                                    p10 t11
                                                        y                                                                                β = ({b,c,d},{y,z})
                                                                                                                  β                      γ = ({c,d,g},{z})
                                                                                                                                         δ = ({e,f},{x,y})

Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012                                                                         7
Behavioral Models




                                                Review A arrived




                                                Review B arrived
              Dissertation submitted                                        Disputation scheduled



                                               Review C arrived




Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012              8
Process Set Abstraction
                                                                                                                  t10
                                                                                                      p12                p11
                                                                                 t13                             e                       t8
                                                        t2                                  p15 t12                               t9 p
                                                                                                                                      10
                                              p2              p3
                                                                                 g                               t11
                                                        a
Net system




                                                                            t5                         p14
                                     p1 t 1                        t4 p 6                                                                      t14 p
                                                                                       p7                         f            p13    p9             16

                                                        t3                   c                  t6
                                              p4              p5                                      p8                t7
                                                        b                                                        d


                               α δ                                                                           β                γ
                               ...
                               ...




                                                                                                                         ...
                                                                                                                 ...
                                                                                                            {α}
                          e2




                                                                                                                                                          abstraction
                                                                                                                                                          Process set
                     c2         c3                                                                                           {β,γ}            {β,γ}
Process




                          a                                                                                  e2
             c1 e1                    e4 c
                                          6
                                                   e5        c7 e6 c8       e7   c9
                          e3
                                                   c                        d                                                  e5               e7
                     c4         c5
                          b                                                                                  e3

                                                                                                            {β}

       Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012                                                                  9
Process Tactic
                                                        (http://en.wikipedia.org/wiki/Battle_of_Borodino)



      A process tactic is a partition of events
                             of a process set abstraction, such that:
                                       {α}
                                        e2         {β,γ}         {β,γ}
                                                      e5            e7
                                        e3

                                       {β}                                         Complex event

   (i) all events in a part can have the same ‘label’, and
   (ii) every two events from distinct parts are in the same causal relation.

Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012                      10
Aligned Process Set Abstractions
                                            α
                    {α}                                          {α}        {α,δ}
                     e2       {β,γ}       {β,γ}                   e2          e4         {β,γ}
                                e5          e7                                            e8
                     e3                                                       e6
                    {β}                          β                          {β,δ}         γ
                      Set abstraction of                            Set abstraction of
                  a process from system (a)                     a process from system (b)

   Two process set abstractions are aligned if and only if:
   (i) there exist tactics of their set abstractions, and
                                        abstractions
   (ii) there exists a mapping between tactics that
        respects alignment and causality.

Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012           11
Tactic Coverage / Isotactics
A system covers the tactic of another system if every process of the latter
   system has a corresponding aligned process in the former system …
                                           α
                         {α}                                {α}     {α,δ}
                          e2     {β,γ}    {β,γ}             e2        e4      {β,γ}
                                  e5        e7                                 e8
                          e3                                          e6
                         {β}                     β                  {β,δ}      γ

    ... and the process alignment relation is closed under process extensions.
                                α
               {α}                               {α} {α,δ}
                e2  {β,γ} {β,γ}                   e2   e4   {β,γ}
                                  {δ}                             {β,δ}
                           e5       e7                                             e8
                  e3                        e11                         e6               e'6
                  {β}                                                 {β,δ}     γ
                                                                                         δ
                                            β
Two systems are isotactic if they cover the tactic of each other
Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012         12
Abstraction in terms of Tactic Coverage
Let S1 and S2 be two systems. An alignment of S1 and S2 is an abstraction
   iff S2 covers the tactic of S1 and the aggregation predicate holds.

                                                          Abstraction?

                                                                   α
                                                                   β
               Select
                         w     Collect    x                                      Study
                                                                                           a
                               product
               product                                                          product
                                 info
          u                                                   v                                            c
                                               Perform                                          Perform
                                               analysis                                         analysis
                               Collect
                                                          z                     Collect
                               market                              γ            market
                                                                                 info
                                info      y                                                b
                                                                   δ
                                         (a)                                              (b)


                                                          Abstraction?
Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012                         13
Abstraction (Example)
                 {α}                                       {α}            {α,β}
                 Select                                                   Collect         {α}         {α,β}
                                                           Select
                                                                          product
                product
                                     {β,γ}                product
                                                                            info
                                                                                       Select
                                                                                                      Collect
                                                                                                      product
                                                                                      product
                                                                                                        info        {γ,δ}
                                      Collect
(a)




                                      market                                                                        Perform
                                       info                                                           {β,γ}         analysis
       {α}             {α,β}                                        {β,γ}                             Collect
                          Collect                                                                     market
       Select                                                       Collect
                          product                                                                      info
      product                                                       market
                            info
                                                                     info




                                                                 {α,β}                     {α,β}
                                                                     Study                   Study
             {α,β}                    {β,γ}                         product                 product             {γ,δ}
(b)




                                      Collect                                                                   Perform
                 Study
                product
                                      market                        {β,γ}                   {β,γ}               analysis
                                       info                                                 Collect
                                                                    Collect                 market
                                                                    market                   info
                                                                     info



 Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012                                    14
Conclusion

 In this work:
       Used experience from past works to develop and motivate concepts for reasoning
       about alignment and (behavior-based) abstraction of process models
       Argued that single-entry-single-exit abstractions preserve isotactics
       Showed cases when the order of transition occurrences and concurrent enablement
       of transitions is preserved by isotactics


 Ongoing and future work:
       Isotactics spectrum (linear vs. branching time & interleaving vs. true concurrency)
       Develop algorithm(s) for checking isotactics
       Discover properties that are preserved by isotactics
       Develop model transformations/abstractions that preserve tactic coverage/isotactics




Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012       15

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Isotactics as a Foundation for Alignment and Abstraction of Behavioral Models

  • 1. 10th International Conference on Business Process Management September 3-6, 2012 | Tallinn, Estonia Isotactics as a Foundation for Alignment and Abstraction of Behavioral Models Artem Polyvyanyy* Matthias Weidlich Mathias Weske BPM Discipline Faculty of Industrial BPT Group Information Systems School Engineering & Management Hasso Plattner Institute Faculty of Science & Engineering Technion University of Potsdam Queensland University of Technology Technion – Israel Institute of Technology Hasso Plattner Institute Brisbane, Australia Haifa, Israel Potsdam, Germany
  • 2. Modeling Mapping Reduction Pragmatics [ Weidlich 2011] Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012 2
  • 3. Process Modeling [ Weidlich 2011] Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012 3
  • 4. Motivation (Structural Abstraction) Abstraction is at the core of model creation, which comprises the mapping and reducing the entities of a problem domain for a certain purpose In process models, abstraction is achieved by means of sub-processes A sub-process in an abstract version of an original process model is a contracted to a single vertex connected, usually single-entry-single-exit, sub-graph of the original model a In stock c d e Receive Ship Send Receive (a) order products bill payment Mapping Make products α = (a,{s,t}) Not in stock b Reducing α β β = (b,{u,v,w}) Purchase u ... Not in stock raw material w Manufacture products Order Make production plan v s t Analyze Check (b) order stock x y z Ship Send Receive products bill payment In stock [ Artem Polyvyanyy, Sergey Smirnov, Mathias Weske: The Triconnected Abstraction of Process Models. BPM 2009: 229-244 ] Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012 4
  • 5. Beyond Structural Abstraction Structural abstraction defines a relation on process models with the intuitive behavioral relation between original models and their abstract versions Do other (behavioral) abstraction relations on process models exist? o Which mappings are allowed? o Which reductions are allowed? o How behavior is preserved? Abstraction? Collect Select Study product product product info Perform Perform analysis analysis Collect Collect market market info info (a) Abstraction? (b) Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012 5
  • 6. Alignment w/o Restrictions Collect e δ product info g α Perform detailed a analysis Study Collect product market Perform c info (a) f initial analysis d γ Evaluate Study analysis market results b Select w Collect x product product info α = ({a},{w,x}) (b) Perform analysis β = ({b,c,d},{y,z}) Collect z γ = ({c,d,g},{z}) market y β info δ = ({e,f},{x,y}) Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012 6
  • 7. Alignment of Petri nets t10 p12 p11 α t13 p15 t12 e t9 p t8 t2 10 p2 p3 g t11 a t5 p14 p1 t1 t4 p 6 t14 p p7 f p13 p9 16 (a) t3 c t6 p4 p5 p8 t7 b d γ δ t10 p11 t2 t3 t4 p2 p4 p5 w x t8 t9 p1 t1 p3 t7 p9 p12 (b) t6 z α = ({a},{w,x}) p6 t5 p7 p8 p10 t11 y β = ({b,c,d},{y,z}) β γ = ({c,d,g},{z}) δ = ({e,f},{x,y}) Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012 7
  • 8. Behavioral Models Review A arrived Review B arrived Dissertation submitted Disputation scheduled Review C arrived Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012 8
  • 9. Process Set Abstraction t10 p12 p11 t13 e t8 t2 p15 t12 t9 p 10 p2 p3 g t11 a Net system t5 p14 p1 t 1 t4 p 6 t14 p p7 f p13 p9 16 t3 c t6 p4 p5 p8 t7 b d α δ β γ ... ... ... ... {α} e2 abstraction Process set c2 c3 {β,γ} {β,γ} Process a e2 c1 e1 e4 c 6 e5 c7 e6 c8 e7 c9 e3 c d e5 e7 c4 c5 b e3 {β} Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012 9
  • 10. Process Tactic (http://en.wikipedia.org/wiki/Battle_of_Borodino) A process tactic is a partition of events of a process set abstraction, such that: {α} e2 {β,γ} {β,γ} e5 e7 e3 {β} Complex event (i) all events in a part can have the same ‘label’, and (ii) every two events from distinct parts are in the same causal relation. Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012 10
  • 11. Aligned Process Set Abstractions α {α} {α} {α,δ} e2 {β,γ} {β,γ} e2 e4 {β,γ} e5 e7 e8 e3 e6 {β} β {β,δ} γ Set abstraction of Set abstraction of a process from system (a) a process from system (b) Two process set abstractions are aligned if and only if: (i) there exist tactics of their set abstractions, and abstractions (ii) there exists a mapping between tactics that respects alignment and causality. Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012 11
  • 12. Tactic Coverage / Isotactics A system covers the tactic of another system if every process of the latter system has a corresponding aligned process in the former system … α {α} {α} {α,δ} e2 {β,γ} {β,γ} e2 e4 {β,γ} e5 e7 e8 e3 e6 {β} β {β,δ} γ ... and the process alignment relation is closed under process extensions. α {α} {α} {α,δ} e2 {β,γ} {β,γ} e2 e4 {β,γ} {δ} {β,δ} e5 e7 e8 e3 e11 e6 e'6 {β} {β,δ} γ δ β Two systems are isotactic if they cover the tactic of each other Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012 12
  • 13. Abstraction in terms of Tactic Coverage Let S1 and S2 be two systems. An alignment of S1 and S2 is an abstraction iff S2 covers the tactic of S1 and the aggregation predicate holds. Abstraction? α β Select w Collect x Study a product product product info u v c Perform Perform analysis analysis Collect z Collect market γ market info info y b δ (a) (b) Abstraction? Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012 13
  • 14. Abstraction (Example) {α} {α} {α,β} Select Collect {α} {α,β} Select product product {β,γ} product info Select Collect product product info {γ,δ} Collect (a) market Perform info {β,γ} analysis {α} {α,β} {β,γ} Collect Collect market Select Collect product info product market info info {α,β} {α,β} Study Study {α,β} {β,γ} product product {γ,δ} (b) Collect Perform Study product market {β,γ} {β,γ} analysis info Collect Collect market market info info Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012 14
  • 15. Conclusion In this work: Used experience from past works to develop and motivate concepts for reasoning about alignment and (behavior-based) abstraction of process models Argued that single-entry-single-exit abstractions preserve isotactics Showed cases when the order of transition occurrences and concurrent enablement of transitions is preserved by isotactics Ongoing and future work: Isotactics spectrum (linear vs. branching time & interleaving vs. true concurrency) Develop algorithm(s) for checking isotactics Discover properties that are preserved by isotactics Develop model transformations/abstractions that preserve tactic coverage/isotactics Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM'12 | September 6, 2012 15