Business Process Modeling: Lecture Notes

Typeset lecture notes for Business Process Modeling (BPM), University of Pisa, academic year 2025/26, taught by Roberto Bruni and Andrea Vandin. The notes cover BPMN and EPC visual notation, Petri nets and workflow nets, occurrence graphs, liveness and boundedness, soundness and structural analysis (invariants, free-choice nets, S/T-systems), process mining, conformance checking, quantitative analysis, and diagnosis of workflow nets. The official course page with the full slide set is on didawiki.

⚠️ Disclaimer. Derived from the Business Process Modeling course materials (Academic Year 2025/2026), MSc in Data Science & Business Informatics, University of Pisa.

These notes are open educational content created by a student. They are not an academic source and may contain inaccuracies. You may freely share, modify, and reuse this material for educational and non-commercial purposes with appropriate attribution. The content is my personal interpretation of the professor's course materials and should not replace official teaching resources. I assume no responsibility for any errors or misinterpretations.

These notes were produced with an AI-in-the-middle workflow: a first human pass, then Claude Code to support formulation, understanding, and rewriting, followed by a final human review.

If you find errors, have suggestions, or spot unintentionally included copyrighted material (which I will promptly remove on notification), contact me at sclfnc@proton.me.

This course is part of the MSc Data Science lecture notes collection (University of Pisa), one repository per course. Clone the whole set with git clone --recursive.

Layout

• main.tex: entry point, in the folder root; identical across the whole notes collection (it only loads the shared preamble and the course file).
• src/housestyle.tex, shared house style: geometry, colors, section and ToC formatting, running heads, and the math environments (theorem, definition, …).
• src/common-preamble.tex: the shared package set, identical across courses.
• src/course.tex, everything specific to this course: title metadata, math macros, the box-free definition/note/example callouts, the TikZ BPMN element styles (bpmn task/gateway/event/flow), the listings style, and hyperref/cleveref, plus the \input{sec/...} list.
• sec/NN_*.tex: section files (the body of the notes), pulled in by course.tex via \coursebody.
• img/: a handful of raster figures (the BPM wheel, the Königsberg bridges, a BPMN thesis example) used in the introduction; all other diagrams are native TikZ, no slide screenshots.
• bpm-notes.pdf: the compiled notes, in the folder root.
• No bibliography: the notes carry no .bib file and use no \cite; sources are listed inline in the introduction's References subsection.

Suspected errors in the official slides are corrected in place and documented in %-comments at the relevant spot.

Build

Build from the folder root:

latexmk main.tex

latexmk runs pdflatex as many times as needed. The compiled PDF is named bpm-notes.pdf; the LaTeX auxiliaries (.aux, .log, .toc, .bcf, .bbl, …) land in the folder root alongside it and are git-ignored (listed in .gitignore). A .latexmkrc in the folder sets this up. To do it by hand instead:

pdflatex -jobname=bpm-notes main && pdflatex -jobname=bpm-notes main

The second pass resolves the table of contents and cross-references. Requires a standard TeX Live installation. Alternatively, upload the folder to Overleaf (New Project → Upload Project), set main.tex as the main document, and compile.

Credits

Written by Francesco Secoli, revised with the help of Claude Code: the slide decks were transcribed and refined into LaTeX, then reworked into standalone notes and verified slide-by-slide against the official PDFs. Based on the Business Process Modeling course (a.y. 2025/26) taught by Roberto Bruni and Andrea Vandin, University of Pisa. Contributions welcome: open an issue or a pull request.

Contents

The notes are twenty sections plus three appendices, in reading order:

#	Section	Topics
1	Introduction	What business processes and BPM are, modelling, tastes of BPMN and process mining, and why formal proofs matter (Euler's theorem)
2	Business Processes	Terminology, products and specialization, process orientation, organizational structures, actors/principals/contractors, cases and procedures
3	Visual notation	Modelling objectives, the BPM lifecycle, BPMN vs .bpmn, tasks and links, control-flow patterns, ambiguity and disambiguation, an insurance-claim example
4	Petri nets basics	Places, transitions, tokens, arcs, the token game, workflow nets, WoPeD, syntactic sugar for split/join, subprocesses, control-flow patterns, triggers
5	Process Mining	The mining framework; cases, events, attributes; discovery, conformance, enhancement; quality criteria; the α-algorithm (ordering relations, footprint matrix); noise and limitations
6	Orchestration and collaboration	Functional goals, orchestration vs choreography, collaboration and compatibility, from question to insight, when process mining makes sense
7	EPC and BPMN	EPC syntax and semantics, BPMN flow objects and swimlanes, typical patterns, lanes and sub-processes, activities and events, collaboration and choreography, data in BPMN
8	From Automata to Nets	Finite automata and DFAs, reshaping automata into nets, multisets, the formal definition of Petri nets, firing sequences
9	Occurrence graphs	Reachability graphs, boundedness, coverability
10	Liveness	Live and dead nodes, deadlock-freedom, the lattice of implications, the four-property checklist
11	Incidence matrices	The incidence matrix, Parikh vectors, the marking equation, monotonicity and its consequences
12	Analysis of Workflow Nets	Behavioural pathologies, the language of a net, soundness, the auxiliary net N*, strong connectedness, a worked repair-service example
13	Sound by construction	Composition by refinement, building blocks, refinement and abstraction, generalised substitution
14	Invariants, S-systems and T-systems	S- and T-invariants and the system properties they certify, strong connectedness via invariants, S-systems and T-systems
15	Analysis of EPC and BPMN	The translation pipeline, straight translation with relaxed soundness, simplified EPCs and free-choice nets, decorated EPCs, the BPMN translation
16	Free-choice nets	Stable sets, siphons and traps, the P/NP complexity background, NP-completeness of liveness, the Rank Theorem for liveness and boundedness
17	Workflow modules	Workflow modules, workflow systems, weak soundness
18	Conformance checking	Four models with naïve fitness, token replay (missing and remaining tokens), diagnostics and drill-down, comparing footprints
19	Quantitative analysis	Cycle-time analysis, theoretical cycle time and efficiency, Little's law, cost analysis
20	Diagnosis for workflow nets	S-coverability, well-structuredness, error / non-live / unbounded sequences, practice with WoPeD
A	BPM cheat sheets	Definitions, properties, general results, and an analysis summary table
B	Process mining hands-on with Disco	Guided walkthrough of process mining with the Disco tool
C	Worked figures	Nets to draw at the exam: soundness, liveness/boundedness, PT/TP handles, S/T-nets and invariants, siphons and traps, the short-circuit N*