Contributed on October 24, 2012

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Isotactics as a Foundation for Alignment and Abstraction of Behavioral Models

Description

There are many use cases in business process management that require the comparison of behavioral models. For instance, verifying equivalence is the basis for assessing whether a technical workflow correctly implements a business process, or whether a process realization conforms to a reference process. This paper proposes an equivalence relation for models that describe behaviors based on the concurrency semantics of net theory and for which an alignment relation has been defined. This equivalence, called isotactics, preserves the level of concurrency of aligned operations. Furthermore, we elaborate on the conditions under which an alignment relation can be classified as an abstraction. Finally, we show that alignment relations induced by structural refinements of behavioral models are indeed behavioral abstractions.

Transcript

10th International Conference on Business Process Management September 3-6, 2012 | Tallinn, EstoniaIsotactics as a Foundation forAlignment and Abstractionof Behavioral ModelsArtem Polyvyanyy* Matthias Weidlich Mathias WeskeBPM Discipline Faculty of Industrial BPT GroupInformation Systems School Engineering & Management Hasso Plattner InstituteFaculty 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 | BPM12 | September 6, 2012 2 Process Modeling [ Weidlich 2011]Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM12 | 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 | BPM12 | 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 | BPM12 | September 6, 2012 5 Alignment w/o Restrictions Collect e δ product info gα 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 infoα = ({a},{w,x}) (b) Perform analysisβ = ({b,c,d},{y,z}) Collect zγ = ({c,d,g},{z}) market y β infoδ = ({e,f},{x,y})Artem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM12 | 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 | BPM12 | September 6, 2012 7 Behavioral Models Review A arrived Review B arrived Dissertation submitted Disputation scheduled Review C arrivedArtem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM12 | September 6, 2012 8 Process Set Abstraction t10 p12 p11 t13 e t8 t2 p15 t12 t9 p 10 p2 p3 g t11 aNet 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 | BPM12 | 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 | BPM12 | 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 | BPM12 | September 6, 2012 11 Tactic Coverage / IsotacticsA 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 e6 {β} {β,δ} γ δ βTwo systems are isotactic if they cover the tactic of each otherArtem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM12 | September 6, 2012 12 Abstraction in terms of Tactic CoverageLet 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 | BPM12 | 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 | BPM12 | 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/isotacticsArtem Polyvyanyy | Isotactics for Alignment & Abstraction | BPM12 | September 6, 2012 15