"Decomposing Alignment- based Conformance Checking of Data-aware Process Models" Massimiliano de Leoni, Jorge Muñoz-Gama, Josep Carmona, Wil van der Aalst PAGE 0 This presentation includes adaptations of slides prepared by Jorge Muñoz-Gama

Process Mining 1

(a; {A = 3000;R = Michael; E = Pete}); (b; {V = OK;E = Sue}); (c; {I = 530;D = OK;E = Sue}); (f; {E = Pete}); Example: A Credit Institute PAGE 3 For such a credit amount, should be interest <450 «Sue» not authorized to perform b: is not Assistant Activity h hasn’t been executed: D cannot be OK (a; {A = 3000;R = Michael; E = Pete}); (b; {V = OK;E = Pete}); (c; {I = 530;D = OK;E = Sue}); (d, {I = 599; D = NOK; E = Sue}); (f; {E = Pete}); (a; {A = 3000;R = Michael; E = Pete}); (b; {V = OK;E = Pete}); (c; {I = 530;D = OK;E = Sue}); (d, {I = 599; D = NOK; E = Sue}); (f; {E = Pete}); (a; {A = 5001;R = Michael; E = Pete}); (b; {V = OK;E = Pete}); (c; {I = 530;D = NOK;E = Sue}); (f; {E = Pete}); (a; {A = 5001;R = Michael; E = Pete}); (b; {V = OK;E = Pete}); (c; {I = 530;D = NOK;E = Sue}); (f; {E = Pete}); Activity d should have occurred, since amount<5000

Conformance General Idea 4 Process Traces Log trace Nonconformity

Alignments Moves in both with incorrect write operations Move in log Move in process

Cost of alignments Each move is associated with a cost Cost of alignment is the sum of the costs of its moves : Cost of reading/writing a wrong value : Cost of “move on log” : Cost of not writing or reading a variable : Cost of “move on model” 2 2

Cost of alignments: some examples 8 10 An optimal alignment: an alignment with the lowest cost

Finding an optimal alignment Undecidable in the general case. If guards are restricted to be linear (in)equations, finding an optimal alignments is Decidable BUT Double Exponential on the size of the model, i.e. the number of activities and data variables. M. de Leoni, W. M. P. van der Aalst "Aligning Event Logs and Process Models for Multi-Perspective Conformance Checking: An Approach Based on Integer Linear Programming“. BPM 2013 F. Mannhardt, M. de Leoni, H. Reijers, W. M. P. van der Aalst. “Balanced Multi-Perspective Checking of Process Conformance”. Software Computing, Springer (Under Review). Also available as BPM Center Report BPM-14-07, BPMcenter.org, 2014.

Finding an optimal alignment: a divide-et-impera approach Beneficial since the problem is exponential!! t1 t2 t3 t4 t6 t5 t1 t2 t3 t4 t6 t5 Decomposed Perfectly Fitting Checking: A model/log is perfectly fitting if and only if all the components are perfectly fitting

Petri Net with Data : Variables and Read/Write Operations Variables Write Operations Read Operations

Each transition is associated with all valid bindings PAGE 11 TransitionGuard Credit Request -- Verify 0.1 * r(A) < w(I) < 0.2 * r(A) Assessment r(V) = true Register Negative Verification r(V) = false AND w(D) = false Inform Requester -- Register Loan Rejection r(D) = false Open Credit r(D) = true

Structural Decomposition 12

SESE (Single-Entry-Single-Exit) Decomposition 13 SESE: set of edges which graph has a Single Entry node and a Single Exit node Refined Process Structure Tree (RPST) containing non overlapping SESEs Unique Modular Linear Time <

SESE does not guarantee Decomposed Perfectly Fitting Checking / 1 Decomposed Perfectly Fitting Checking: A model/log is perfectly fitting if and only if all the components are perfectly fitting The problem is in the boundary places or variables No reflection on the log A partition with only transitions shared among components (neither places, nor variables, nor arcs) Transitions have reflection on the log

SESE does not guarantee Decomposed Perfectly Fitting Checking / 2 Create a ‘bridge’ for each shared place 15

Implementation Available in the package DataConformanceChecker

Experiments Generating different event logs with 5000 traces with a different average trace length This ensured by enforcing a larger number of credit renegotiations 20% of the transition firings are so as to not satisfy the guards

Example of the SESE-based Algorithm

Results: an exponential reduction of the computation time

Projection on the model #correct(t,DPN) = number of moves in both without incorrect write operations for t in the alignments between each log trace and DPN #total(t,DPN) = number of moves for t in the alignments of each log trace and DPN

Experiments with a real-life process Process enacted by a Dutch governmental agency to deal with unemployment benefits Checked the conformance against an event log consisting of 111 traces Process Model validated with process analysts of the agency Without Decomposition: seconds With Decomposition: seconds -99.9%

Conclusion Finding an alignment is exponential in the model size To speed the computation: 1.Decompose the model in submodels 2.Alignment each trace with each submodel The decomposition needs to be valid: Any trace is fitting the entire model if and only if it fits all smaller fragments.