Timed Automata |
September - December 2021 |
Timed automata are an extension of finite automata to deal with
timing constraints between actions. They offer
challenging language theoretic as well as verification
questions. A
number of formal techniques have been employed in the study of
this model. The goal of this course is to understand this
model and get acquainted with the different techniques
used in its analysis.
The skills developed during the course are
fairly general and the hope is that they could be used in the
analysis of various other models.
Previous versions of this course can be found here: 2020
2019
Mon, Wed: 09:10 - 10:25
Lectures will be delivered via Zoom. Please join Moodle course page for the link.Module 1: Basics | |||||
Lecture 1 | 20.09.2021 (Mon) | Timed languages, timed automata, closure properties | Slides | Video | Problem Sheet 1 |
Lecture 2 | 22.09.2021 (Wed) | Untiming construction: why a naïve construction is wrong, adding clock information to states, a neighbourhood equivalence | Slides | Video | Problem Sheet 2 |
Lecture 3 | 27.09.2021 (Mon) | Untiming construction: discussion of Problem Sheet 2, properties of the neighbourhood equivalence, neighbourhood automaton | Slides | Video | |
Lecture 4 | 29.09.2021 (Wed) | Untiming construction: the region equivalence and region automaton | Slides Notes | Video | Problem Sheet 3 |
Lecture 5 | 04.10.2021 (Mon) | Discussion of Problem Sheets 1 and 3, some new problems | Slides | Video | |
Lecture 6 | 11.10.2021 (Mon) | Universality is undecidable | Slides | Video | Problem Sheet 4 |
Lecture 7 | 13.10.2021 (Wed) | Deterministic Timed Automata | Slides | Video | |
Lecture 8 | 18.10.2021 (Mon) | Event-Recording Automata | Slides | Video | Paper |
Lecture 9 | 20.10.2021 (Wed) | Event-Predicting Automata, Event-Clock Automata | Slides | Video Part 1 Part 2 | |
Lecture 10 | 25.10.2021 (Mon) | ECA to NTA, Expressiveness of ERA, EPA, ECA with DTA and NTA | Slides | Video | Problem Sheet 5 |
Module 2: Verification | |||||
Lecture 11 | 27.10.2021 (Wed) | Networks of timed automata, Introduction to zone based algorithm | Slides | Video | |
Lecture 12 | 01.11.2021 (Mon) | Zone graphs: examples, formal definition, some properties | Slides | Video | |
Lecture 13 | 03.11.2021 (Wed) | Getting finite truncations of zone graphs |
Slides
Notes |
Video | Problem Sheet 6 |
Lecture 14 | 10.11.2021 (Wed) | Discussion of Problem Sheets 4, 5 and 6 | Slides | Video | |
Module 3: Advanced topics | |||||
Lecture 15 | 15.11.2021 (Mon) | Universality is decidable for one-clock timed automata - Part I | Slides | Video | |
Lecture 16 | 17.11.2021 (Wed) | Universality is decidable for one-clock timed automata - Part II | Slides | Video | |
Lecture 17 | 22.11.2021 (Mon) | Universality is decidable for one-clock timed automata - Part III | Slides | Video | |
Lecture 18 | 24.11.2021 (Wed) | Timed Automata with diagonal constraints - Part I |
Slides Notes |
Video | |
Lecture 19 | 29.11.2021 (Mon) | Timed Automata with diagonal constraints - Part II |
Slides Notes |
Video | |
Lecture 20 | 1.12.2021 (Wed) | Alternating Timed Automata: model, example, acceptance game | Slides | Video | |
Lecture 21 | 06.12.2021 (Mon) | Alternating Timed Automata: closure properties, emptiness and one-clock restriction, expressive power of 1-ATAs | Slides | Video | |
Lecture 22 | 08.12.2021 (Wed) | Alternating Timed Automata: 1-ATA incomparable with 2-NTA | Slides | Video | |
Lecture 23 | 13.12.2021 (Mon) | Alternating Timed Automata: Emptiness for 1-ATA is non-primitive recursive | Slides | Video | |
Lecture 24 | 15.12.2021 (Wed) | Updatable Timed Automata: syntax, examples | Slides | Video | |
Lecture 25 | 20.12.2021 (Mon) | Updatable Timed Automata: emptiness problem | Slides | Video | |
Lecture 26 | 22.12.2021 (Wed) | Updatable Timed Automata: expressiveness | Slides | Video |