Theoretical Foundations of the UML


  • 08.8.2016: The results of the exam will soon be made available through campus office. The exam inspection will take place on Monday, August 15, at 15:00h in our seminar room (Building E1, Room 4201b).
  • 01.8.2016: There has been some confusion with the timing of the exam. The dates and times announced on this website are correct. The first exam takes place on Thursday, August 4 at 13:00h in lecture hall AH I.
  • 20.7.2016: Please find the results of the evaluation of the lecture and the exercise class below.
  • 15.7.2016: During the lecture on Tuesday, July 19, Prof. Katoen will present an old exam.
  • 07.7.2016: There will be no exercise class today.
  • 28.6.2016: The word (locally) in the statement “Every (locally) communication-closed MSG is regular.” on slide 7 of Lecture 13 needs to be removed.
  • 27.6.2016: An old exam is now available in the Exam section on this page.
  • 26.5.2016: The last example on page 10 of the slides of lecture 6 was erroneous, and has now been fixed.  A new version of the slides is on-line.
  • 17.5.2016: By majority vote, the next exercise class will take place on Friday, May 27 at 10:15 in Room 9U09.
  • 12.5.2016: Please indicate your preferences for the date of the next exercise class here until Sunday, May 15. We will try to arrange a date which is most convenient for most of you. However, please keep in mind that we also need to organize a room, so the date we will arrange might not coincide with the majority vote.
  • 03.5.2016: There was a problem with the campus office settings for this course which affected the exam registration for some of you. That issue should be fixed now. The deadline for exam registration is May 20, but we urge you to register as soon as possible (just to be on the safe side if any further issues should arise). If you still experience problems registering, please let us know as soon as possible.
  • 28.4.2016: There will be no lecture and exercise class next week.
  • 19.4.2016: The exercise class is now shifted to 16:15 – 17:45 (still in room 9U09 on Thursdays).
  • 19.4.2016: The first exam and re-exam are scheduled on 4th, August and 22th, September, respectively.
  • 18.4.2016: You can register yourself for the exercise class in Campus Office (first after you have logged in) under Theoretical Foundations of the UML (FUML) (Übung (Ü)) with the link “Zum klassischen Anmeldeverfahren” now.
  • 11.4.2016: The lecture will start on Thursday, April 4, at 8:30h in Room 5056 (Building E2). The first exercise sheet will be handed out on Thursday, April 21, and the first exercise class will be given on Thursday, April 28, also in Room 9U09.
  • 05.4.2016: We are online!


Type Day Time Hall Start Lecturer
Lecture Tue 12:15 – 13:45 9U09 19.4. Katoen
Thu 08:30 – 10:00 5056 14.4. Katoen
Exercise Thu 16:15 – 17:45 9U09 28.4. Kaminski, Wu


Content and Motivation

The Unified Modelling Language (UML) — more generally, model-driven engineering — plays an important role in modern software design.  The UML basically consists of a set of different notations, each notation focused on a specific aspect of the software system at hand.  The aim of this course is to consider some major fragments of the UML: sequence diagrams, hierachical state machines (also known as Statecharts), and the OCL (short for Object Constraint Language).

  • Sequence diagrams specify the interaction patterns between the system components and are a popular elicitation technique for requirements engineering.


  • Hierachical state machines and message passing automata are used to describe the behaviour of system components, and are intensively used during the system’s design phases, e.g., in the fields of avionics and automotive industry.


  • Finally, the OCL allows to specify properties of system components, ranging from pre- and postconditions to invariants and more complex properties

Aims of this Course

The aim of this course is to treat the theoretical underpinnings of the aforementioned UML fragments.  In particular, we will present the theories required to:
  1. Clarify and make precise the semantics of the (treated fragments of the) UML;
  2. Reason about the basic properties of UML models;
  3. Algorithms to allow for the verification of such properties on UML models
It is our firm belief (and experience) that a solid theoretical underpinning is of prime importance to obtain automated tools (such as MSCan) that produce reliable, i.e, verifiable results.


Although the name UML might suggest differently, this is a theoretical course!  That is, a solid basis in algorithms and data structures, automata theory, and a bit of theoretical computability and complexity theory is needed to be able to follow this course.

The course will cover for instance, formal semantics (how to precisly lay down the meaning of UML diagrams) and formal verification (is checking certain properties on UML diagrams decidable, and if so, efficiently decidable).

Basic knowledge of the undergraduate courses of the first two years:
  • Automata Theory
  • Mathematical Logic
  • Discrete Mathematics
  • Computability and Complexity Theory

Slides and Exercise Sheets

Date Lecture Topic Handout/Slides Exercises Additional material
April 14+17 1+2 Intro + Message Sequence Charts



April 19  3 Races



April 21  4 Message Sequence Graphs



 April 28  5 Emptiness of MSG intersection  blackboard lecture
 May 10  6 Compositional MSGs



 e3 proof
 May 12  7 Safe CMSGs  blackboard lecture
 May 24  8 Communicating FSMs

no handout (due to overlays)


 May 31  9 Bounded MSCs and CFMs



 June 2  10 Realisability (1)



 e5 proof
June 7  11 Realisability (2)
June 9  12 Safe Realisability



 e6 proof
June 16  13 Regular MSGs



June 21  14 Realising local choice MSGs



June 28  15 Propositional dynamic logic



June 30  16 Propositional dynamic logic
July 12  17 Statecharts



July 14  18 Statecharts semantics (1) slides_lecture_18
July 19  19 Statecharts semantics (2) / Old Exam slides_lecture_19



Date Time Location
First exam Thu,  4. August, 2016 13:00 – 15:00 AH1
Re-exam Thu,  22. September, 2016 13:00 – 15:00 AH1

An old exam with solutions is available here.

Evaluation results

Further information

  • The course will be entirely given in English. The slides and other course material will also be in English.
  • There are no lecture notes (yet); the course material will consist of the slides.
  • An examination will take place at the end of the course.

Background Literature and Interesting Links

  • Jos Warmer and Anneke Kleppe, Object Constraint Language, The: Precise Modeling with UML. Addison Wesley, 2001.
  • D. Harel and M. Politi, Modeling Reactive Systems with Statecharts: The STATEMATE Approach, McGraw-Hill, 1998.
  • Benedikt Bollig – Formal Models of Communicating Systems, Springer, 2006 (Chapter 7, 8 and 9)
  • The course will however be mainly based on recent scientific papers.