Operator

Short Description

Operator is a subclass of process element. An operator determines the process’s behavior in case its control-flow is split up into or joined from several execution branches. For each subtype exists a Split- and a Join-Operator. The split can either represent an exclusive or non exclusive choice between different alternative branches, or a parallel execution of several process branches. The join merges the split up control flow considering the logic used in the split. As a result, the join operator needs to be of the same type as the logical operator that initially split the control flow. [1]
Following that logic there are three different subtypes of the operator process element:

XOR Operator: Exclusive choice
OR Operator: Nonexclusive choice
AND Operator: Parallel Execution

Operators can also be altered by assigning 0 to n attributes to it.

Semantic Representation

In the following an operator is called connector.

A connector C is a finite and pairwise disjoint set. It is a part of an EPC = (E, F, P, V, l , A ) and is represented in the mapping l: C→ {and, xor, or}.

A connector is also defined as a node, as it is part of the union N = E ∪ F ∪ P ∪ C.[2]

Following subsets are defined:

• J = {c ∈ C | |•c| > 1 and |c•| = 1} as the set of join connectors,
  S= {c ∈ C | |•c| = 1 and |c•| > 1} as the set of split-connectors.[3][4]

Following requirements are made on connectors so an EPC can be called relaxed syntactically correct:

• There are no connector cycles, i.e. ∀a, b ∈ C : if a ≠ b and a → c → b, then b → c → a does not exit.

• Connectors have one incoming and multiple outgoing arcs or multiple incoming
  and one outgoing arc. ∀ c ∈ C : (|•c| = 1∧ |c•| > 1) ∨ (|•c| > 1 ∧ |c•| = 1).

• Connectors must have either functions, process interfaces, or fe-connectors in the preset and events or fe-connectors in the postset;
  or events or ef-connectors in the preset and functions, process interfaces, or ef-connectors in the postset:
  ∀c ∈ C: (•c ⊆ (F ∪ P ∪ CFE))
  ∧ c• ⊆ (E ∪ CFE)∨ (•c ⊆ (E ∪ CEF )
  ∧ (c• ⊆ (F ∪ P ∪ CEF)).[5]

• After an event, no xor/or connector is allowed.[6]

References

• [*1] M. Fellmann, S. Bittmann, A. Karhof, C. Stolze, and O. Thomas, “Do We Need a Standard for EPC Modelling? The State of Syntactic, Semantic and Pragmatic Quality,” in 5th International Workshop on Enterprise Modelling and Information Systems Architectures (EMISA), 2013, pp. 103–116.

• [*2] Ekkart Kindler "On the semantics of EPCs: resolving the vicious circle", Data & Knowledge Engineering - Special issue: Business process management archive Volume 56 Issue 1, 2006, p. 28.

• [*3] Van der Aalst, "Formalization and verification of event-driven process chains" Information and Software Technology 41, 1999, pp. 639-650
• [*4] Mendling: Event Driven Process Chains - Metrics for Process Models, Volume 6 of the series Lecture Notes in Business Information Processing, 2009, pp. 17-57.
• [*5] K. van Hee, O. Oanea, N. Sidorova, "Colored Petri Nets to Verify Extended Event-Driven Process Chains", OTM Confederated International Conferences "On the Move to Meaningful Internet Systems", 2005, pp. 183-201.

• [*6] M. Nüttgens, F. J. Rump "Syntax und Semantik Ereignisgesteuerter Prozessketten", Prozessorientierte Methoden und Werkzeuge für die Entwicklung von Informationssystemen, Proceedings des GI-Workshops und Fachgruppentreffens, 2002, pp. 65-77.