An amalgam of rich modeling notations have been used and proposed by academics in the process mining literature. Artifact-centric processes, Proclets, CPNs, Petri nets with Data, Object-Centric Petri Nets are examples of these notations. For example, these modeling notations allow to describe interaction of multiple case instances (objects) in single models.
On the contrary, in the industry looks like process mining vendors have not followed this trend initiated by the academia. Most of process mining tools still resort to directly-follows graphs (DFG) to describe single-case process models.
In the penultimate chapter of the book "Process Mining in Action" (Reinkemeyer, 2020), van der Aalst was invited to give his view about the development of the process mining discipline. Among his statements, he criticizes that, albeit in significant advances in research, vendors still resort to DFGs.
The limitations of the DFGs are fairly explained in "A Practitioner's Guide to Process Mining: Limitations of the Directly-Follows Graph" (van der Aalst, 2019).
In the related work section of paper "Discovering Object-Centric Petri Nets" (van der Aalst and Berti, 2020) they merely mentioned one vendor which makes the exception, IBM. The company proposed in an old tool called IBM's Flowmark (1999) a model for handling multiple sub-cases into a single notation. However, I do believe there might be other proposals from vendors out there.
Thus, in this post I would like to inquiry: Which other commercial tools of process mining make use of high-level process modeling notations? (Even if they are informal notations, it would be interesting to find out proposals and their relevant features, if any)
I am wondering why DFG's supposed to have any restrictions. Following is an edited copy of my post in another discussion:
"In 2020, I invented a three-dimensional topological sorting algorithm which I call topological-triple. Using three topological orderings which are tightly coupled, I can conclude given any two propositions of a domain one implies (or implied by) the other, or not (maybe is out of question). Also, being able to claim unambiguously “they are not related to each other in this domain” is worth mentioning. Recently the algorithm covers also cyclical implications, i.e. an implication can refer to another which is already used in the discourse (I am not joking). Another advantage of the algorithm is to decompose the domain in partitions of “Single Point of Control” on the flight. The algorithms’ complexity is linear for insertion of a new implication based on the number of already known propositions. The data structure which stores the result explicates all paths of the discourse. (...)
I will discuss the details of a reference implementation in
https://saiconference.com/FICC.
The paper is titled “Topology and Structure of Directed Acyclic Graphs”. A preliminary version can be found here:
Preprint Iterable Topology of a Directed Acyclic Graph
and here:
Preprint Structure of Directed Trees - A Two-Dimensional Topological Sorting
.It is an extension of the last-mentioned paper."
And a remark:
"... the domain will be represented in an and/or directed graph, a kind of Petri‑Net without tokens, but similar in its semantics."
will continue ...
Currently I am revisiting an article from van der Aalst et al. titled:
"Configurable process models: experiences from a municipality case study"
My aim is to demonstrate that an alternative approach based on topological-triple would be a superior one. I can share early slides of the presentation.
Furthermore, I have a presentation (unfortunately in German) how an alternative model to the one described in:
"Business Process Mining: An Industrial Application" would look like (also from van der Aalst et al.). I can send a private copy, if you are interested.
Directed graphs are probably the most powerful and versatile vehicle to model binary relations. They are free from any restriction, except rigorous enforcement of the rule of transitivity, and the principle “same objects have one and the same meaning”
You should only use them in their full flexibility, and rigorous semantics.
Dear Enis Olgac ,
Thanks a lot for your detailed reply!
A common limitation with directly-follow graphs (transition systems, finite-state machines) is that they are "sequential" models. They do not correctly capture concurrency. The number of transitions exponentially growths when one wants to describe possible interleaving/parallelism between activities (e.g., "a" can be executed before "b" and vice-versa). This is why, for example, most of process mining algorithms in the literature are based on Petri net models.
Yet, commercial tools prefer simplicity, and this why user-friendly sequential models (in the form of directed graphs) are preferred than Petri net-like models (where concurrency is nicely captured or where we can describe resources of different types, like colored Petri nets). The reason of my inquiry is to find exceptions to this tendency. That is, examples in the industry that have used rich concurrent models in process mining commercial tools for describing interaction between objects in a system.
Looks very interesting the model you write about! so I will check about such "topological triples"! Definitely I will check the material you share, and write you again soon. If they indeed are applicable and a potential model within a process mining project, I will consider them in my research work!
Julio Carrasquel
Let me define my understanding of concurrency:
Given two events e1, and e2 in G representing before/after relationships among two events, if there exists no path in G from e1 to e2, or e2 to e1 then e1 and e2 are concurrent. In other words, they are not dependent on each other, or “they are disconnected” so to say. The topological-triple algorithm is designed to conclude correctly and guaranteed whether two events are connected, or disconnected, even if G is cyclic.
... to be continued
But what if there is a third event e3, which is after e1, and after e2. There is no way to represent whether e3 is after both, or only one of them in G. You have two choices at this point:
1. You can choose to implement some artificial mechanisms which for sure effect the semantics of G, especially transitivity. In this case you have to reinvent, and reimplement transitivity (to my opinion this is the case if you use Petri‑nets).
2. You can impose another directed graph G’ on top of G, where vertices of G’ are sort of connectors (they may even be anonymous). G’ is an “And” graph, and G is an “Or” graph as far as their inbound edges are concerned. The tails of inbound edges events are "or" related. The tails of inbound edges of connectors are "and" related. Outbound edges of connectors, and events specify transitive relations.
In case (2) you have a directed graph (G + G’). It is an “And/Or” graph. All known properties of directed graphs are still applicable, especially transitivity.
Topological-triple can decide on the concurrency (dependency) of events under the restrictions defined by the connectors.
I used this notion in:Presentation Broadcast Communication using Distributed Ledger Technology
I am afraid, there I didn’t explain the underlying concept as explicitly as now.
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