Notations:

- transition systems;

- petri nets;

- workflow nets;

- YAWL;

- BPMN;

- EPC;

- Causal Nets;

- IDEF0

- UML Use Case Diagrams and Activity Diagrams

See Process Mining: Data Science in Action by Aalst 2016 for example

ARIS

It is difficult to answer your question as there is no context for the question. What level of process abstraction are you modeling? Requirements? Solution design at a high-level for architecture pattern selection? Solution design at a lower level for solution technology selection?

I have been doing this in industry since 1995. The base approach is graphical with directed cyclic graphs. From a notation standpoint I used a modified graphical representation that is a combination of elements from UML Activity Models and BPMN for requirements level of abstraction. Moving to the design levels extends the requirements notation with additional modeling elements to capture design decision details.

There are modeling elements from UML that I do not use because they do not help cognitive effectiveness in communication within the team. I do not use swim lanes or UML Use Cases in any industry project.

If you are interested in real industry examples see my dissertation:

https://www.se-rwth.de/phdtheses/Diss-Matheson-A-Methodology-for-the-Elicitation-and-Specification-of-Requirements-for-Agile-Model-driven-Engineering-of-Large-Software-Solutions.pdf

tems, and another are new to me. I'll review them. Thank you Marek Spányik

ARIS is another new to me. Thank you Biplab Santra

Thank so much Dan Matheson , I forgot to mention the context. Actually, what I want is to know the languages that exist and if you have ever used them, all the better. It doesn't matter the context or the level of abstraction. I will review the document you share me. Thank you again.

Dan Matheson, I think you are completely on the right track with the Directed Graph approach. I am not sure whether any particular language is needed to describe the model, though. In a series of presentations, I tried to explain a novel approach dealing with directed graphs in general. It also includes a second look at a case study by Aalst et al. Presentation Topology and Structure of Directed Graphs - How to Deal with Cycles

Currently, I am preparing a new presentation dealing with Resource Constrained Project Scheduling Problem. I believe (RC)PSP and Process Modeling are two aspects of the same. Please note that I am able to use And/Or graphs in modeling, which makes life a lot easier compared to Petri nets. Here is an example:

Presentation Topology and Structure of Graphs - Job-Shop Scheduling

It would be interesting to see how you approached the specification aspect in your dissertation.

Enis Olgac, I shall look at your references, thank you.

The key with cycles (rework arcs) is that they must be strongly connected graphs. My team discovered this while building (1993-1995) a commercial workflow engine, the Workflow Module of the HP WorkManager product. The processes were defined via a graphical UI. My contribution to workflow standards in the WfMC and the OMG (1997-2000) further validated the directed graph approach. In the approximately 200 industry processes I have been involved in, 100% had at least one rework arc for a cycle and 98% had concurrent tasks.

Dan Matheson, I am the inventor of IBM's program understanding tool ASMPUT. There I was using techniques based on strongly connected graphs in order to analyze loops in control-flow (1992-1996). Cycles (loops) were one of the most complex issues.

Two years a go, I realized that every cyclic graph has an acyclic skeleton. Since then, I am using the more general concept of "reachability" (connectedness) to identify cycles (loops) instead of paths. A prerequisite to use this technique is to be able to explicate the true "topology" of the graph (a single topological ordering is not sufficient). It is not difficult to explain it, if one takes "chicken and egg" dilemma as an example.

I am not sure whether this is the right place for further discussion. I would be happy to meet in a video conference, or in a private conversation.

By the way,

Presentation Topology and Structure of Graphs - All Paths and "Seven Brid...

Presentation Topology and Structure of Directed Graphs - DNA Sequencing

are two examples of how this novel technique can be used.