Mikołaj Bojańczyk
2023/2024
Złożoność Obliczeniowa / Computational Complexity 2023/2024
A course on computational complexity for 4th year students (1st year of MSc programme). Previous iterations of this course: 2022/2023 and 2020/2021Języki, automaty i obliczenia II • Advanced topics in automata
Wykład przestawia wybrane tematy o automatach. Większość wykładu oparta jest na skrypcie Automata Toobox. W razie konsultacji zapraszam na konsultacje do mnie oraz do Lorenza Clemente.Zasady zaliczenia
Są dwie oceny z przedziału 2–5: ustny i zadania domowe. Ostateczna ocena to średnia ważona: 2/3 * ustny + 1/3 * zadania. Poniżej jest 11 tematów z pytaniami egzaminacyjnymi. Na egzaminy ustny można sobie wybrać podzbiór.- na ocenę 5 trzeba się nauczyć 9 tematów
- na ocenę 4 trzeba się nauczyć 6 tematów
- na ocenę 3 trzeba się nauczyć 4 tematów
Spis wykładów i tematy egzaminacyjne
Algorytm Angluin. Materiał: rozdział 15 w książce Toolbox. Pytania na egzamin: • przedstaw algorytm Angluin Automaty ważone i liniowe Materiał: rozdział 8 w książce Toolbox Pytania na egzamin: • pokaż, że automaty ważony i liniowe są równoważne • przedstaw algorytm równoważności dla tych automatów Automaty wielomianowe Materiał: rozdział 11 w książce Toolbox Pytania na egzamin: • czym są automaty wielomianowe • jak rozstrzyga się ich równoważność Arytmetyka Tarskiego Materiał: rozdział 10 w książce Toolbox. Treść tablicy na wykładzie Pytania na egzamin: udowodnij rozstrzygalność teorii pierwszego rzędu dla ciała liczb rzeczywistych Zbiory orbitowo skończone. Treść tablicy na wykładzie Materiał być może zbyt obfity: książka Slightly Infinite Sets Pytania na egzamin: co to jest zbiór orbitowo skończony • jak się rozstrzyga niepustość dla automatów orbitowo skończonych Przestrzenie wektorowe orbitowo skończone Treść tablicy na wykładzie Pytania na egzamin: co to jest przestrzeń wektorowa orbitowo skończona • udowodnij, że łańcuch podprzestrzeni są skończone Systemy dodawania wektorów Materiał: rozdział 9 w książce Toolbox Pytania na egzamin: udowodnij nierozstrzygalność problemu stopu dla maszyn dwulicznikowych • udowodnij rozstrzygalność problemu "coverability" dla systemów dodawania wektorów Parsowania gramatyk w czasie mnożenia macierzy Materiał: rozdział 12 w książce Toolbox Pytania na egzamin: przedstaw algorytm parsowania korzystający z mnożenia macierzy Determinizacja ω-automatów Materiał: rozdział 1 w książce Toolbox Pytania na egzamin: przedstaw podstawowe modele automatów dla ω-słów, czyli deterministyczne/niedeterministyczne automaty z warunkiem Büchiego/Mullera/parzystości • udowodnij determinizację (do warunku Mullera) Gry nieskończone Materiał: rozdział 2 w książce Toolbox Pytania na egzamin: udowodnij pozycyjną determinację gier z warunkiem parzystości Twierdzenie Rabina Materiał: rozdział 5 w książce Toolbox Pytania na egzamin: udowodnij twierdzenie Rabina, zakładając wyniki z dwóch poprzednich wykładów.
Przekształcenia automatowe • Transducers
This is the page for a transducer course, given at the University of Warsaw in 2024. The tutorials are by Aliaume Lopez, you can find the problems here. Your final grade will be a combination of: (1) an oral exam at the end of the semester; (2) homeworks.Lectures
Mealy machines
Slides- Definition of Mealy machines
- Closure under composition
- The Krohn-Rhodes theorem
Rational functions
Slides- Unambiguous nondeterministic automata with output
- Eilenberg Bi-machines
- Their equivalence
- A Krohn-Rhodes decomposition
- Deciding equivalence
Enter logic
Slides- MSO = regular languages
- MSO relabelings = letter-to-letter rational
- the first-order fragment of MSO
Two-way automata
Slides- Two-way automata with output
- Closure under pre-composition
- Decidable equivalence
MSO transductions
Slides- Definition of MSO transductions
- Equivalence with previous two models
Streaming stream transducers
Slides- Definition of copy less streaming stream transducers
- Equivalence with two-way automata with output
- The copyful version, and decidability of equivalence for it
List functions
Slides- Definition of the linear list functions
- Their first-order fragment
- Proof that they define the same functions as two-way transducers
Polyregular functions 1
Slides- Polynomial Krohn-Rhodes primes
- Polynomial list functions
- For transducers
Polyregular functions 2
- Pebble transducers
- λ-calculus
Polynomial interpretations
- String-to-string MSO interpretations
- Proof that they define exactly the polyregular functions
2022/2023
Złożoność Obliczeniowa / Computational Complexity 2022/2023
A course on computational complexity for 4th year students (1st year of MSc programme).Automata, Logic and Games 2023
This is a course about the interplay of automata, logic and games. Lecture: Wednesday 10:15, room 5840 Tutorial: Wednesday 12:15, same room The automata are finite automata, but often on objects that are not necessarily finite words. The logic is usually monadic second-order logic. The point is that the automata and the logic define the same languages. The games are infinite duration games, which appear as technical tool in the analysis of automata and logics on infinite objects. I will also use semigroups, as a third approach to defining languages.2021/2022
Automata, logic and games
This is a course about the interplay of automata, logic and games. The automata are finite automata, but often on objects that are not necessarily finite words. The logic is usually monadic second-order logic. The point is that the automata and the logic define the same languages. The games are infinite duration games, which appear as technical tool in the analysis of automata and logics on infinite objects. I will also use semigroups, as a third approach to defining languages.2020/2021
Computational Complexity / Złożoność obliczeniowa 2020/2021
A course on computational complexity for 4th year students (1st year of MSc programme).A tutorial on logic, biased towards automata, for the TCFS programme at Simons
This is a 3 part tutorial about logic. It is organised around algorithms for checking if a formula is true in a model.There are two central variants of this problem. In the model checking problem $$M \stackrel ? \models \varphi,$$ we are given the model and the formula, and we want to know it the formula is true in the model. In the satisfiability (dually, validity) problem $$? \models \varphi$$ we are only given the formula, and we want to know if it is true in some (dually, every) model (perhaps from some fixed class of models). There are three parts of the tutorial (each set of slides contains a soundtrack):- Part 1 (slides ) discusses the variant of the model checking problem where the model is fixed and only the formula is given on the input. (This is also known as deciding the theory of the model.) I will particularly focus on cases where the problem can be solved using automata, and hence the corresponding logic is going to be monadic second-order logic, which is an old friend of automata.
- Part 2 (slides) discusses the satisfiability problem. Here, again, the main focus is on variants of the problem that can be solved using automata, namely monadic second-order logic on words, trees and graphs of bounded treewidth.
- Part 2 (slides) discusses the variant of the model checking problem where the formula is fixed and the model is the input. Apart from results that use automata (mainly Courcelle's theorem about MSO model checking on graphs of bounded treewidth), I will also discuss some results about first-order logic on sparse graph classes.
2019/2020
Transducers and their Krohn-Rhodes decompositions
This is a course on transducers, given before the Trends in Transformations workshop at FSTTCS 2019. The course covers rational, regular and polyregular string-to-string functions. A special emphasis is made on theorems a la Krohn-Rhodes, which decompose complicated functions into simpler prime functions.- Mealy machines, the classical Krohn-Rhodes theorem, and its corollaries for sequential and rational functions (slides).
- Regular functions, and some of their equivalent representations (two-way transducers, mso transductions, streaming string transducers, and regular list functions). The prime regular functions (slides).
- Polyregular functions, and some of their equivalent representations (pebble transducers, for transducers, functional programs, mso interpretations). The prime polyregular functions (slides).
Algebraic language theory 2020
This course is about an alternative approach to regular languages, where one uses semigroups and monoids (and more fancy algebraic structures) instead of automata.Soft skills
These are some slides for my Scientist's Workshop lecture.2017/2018
Algebraic language theory (automaty a półgrupy)
This course is about an alternative approach to regular languages, where one uses monoids (and more fancy algebraic structures) instead of automata. I use notes from this lecture, but I hope to create a new version in pdf for this one (this has not materialised, I'm sorry).Advanced Topics in Automata 2017/2018 (Języki, Automaty i Obliczenia 2)
This lecture is a choice of slightly more advanced topics from automata theory.2016/2017
Advanced Topics in Automata 2016/2017 (Języki, Automaty i Obliczenia 2)
This lecture is a choice of slightly more advanced topics from automata theory. The lecture is on Tuesdays, 12:15 in room 5820. The exercises are on Wednesdays, 16:15 in room 5820, with Wojciech Czerwiński. Here is a plan of the lecture. There was a similar lecture last year. Here are the topics for this year:- automata on infinite words: determinisation
- games of infinite duration: the Büchi-Landweber theorem
- distance automata: decidability of limitedness
- treewidth and mso: Courcelle's theorem
- learning automata: the Angluin algorithm
- transducers
Infinite alphabets
This is a lecture on automata (and later other devices) that operate on infinite alphabets. The lecture is on Wednesdays at 12:15 in room 4060. The exercises are on Mondays at 14:15 in room 5050. The lecture and exercises are shared by Mikołaj Bojańczyk and Sławomir Lasota. Lecture notes Homework assignments ExamHere is an overview of the course Data words and their automata In the first half of the lecture, we discuss some concrete models, typically involving registers. The emptiness problem for most powerful of the models, data automata, will as hard as the famous reachability problem for vector addition systems, and the lecture will contain a description of the latter.
- Introduction to automata with registers
- Alternating automata with registers
- Data automata
- Logic on data words
- Reachability for vector addition systems
- Sets with atoms and orbit-finiteness
- Automata in sets with atoms
- Atoms with structure other than equality
- Oligomorphism
- What is a computable function?
- Turing machines with atoms
Lipa
Lipa summer school 2017 (Warsaw, July 3-6)
The Lipa Summer School is a school on topics connected to logic in computer science. It is part of this grant. It was held in Warsaw, July 3-6 2017. The school had 4 mini-courses given by:- Stephan Kreutzer (Berlin) Algorithmic meta-theorems (videos: 1, 2, 3, 4)
- Joël Ouaknine (Saarbrücken) Decision Problems for Linear Recurrence Sequences (videos: 1, 2, 3, 4)
- Moshe Vardi (Rice) Linear-time verification and synthesis (videos: 1, 2, 3, 4)
- Mikołaj Bojańczyk (Warsaw, organiser) What is a recognisable language? (videos: 1, 2, 3, 4)
Dates
May 30 Registration with request for student accommodationJune 20 Registration without request for student accommodationJuly 3-6 School
Local information
The school was held at the University of Warsaw, in the Center of New Technologies, whose address is Banacha 2c. Be careful about the map on the Center's page, it's wrong, use the one below.
Picture of the conference venue and map below
A taxi from the airport should be around ≤ 20 PLN during the day (the official taxi queue is when you leave the airport, don't go with the people who whisper "taxi, taxi"). Here is a link for accessing the school from the airport using public transport (bus 175 or 188).
The school is part of the grant Lipa that has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 683080).
Lipa Summer School 2018 (June 25-28)
The Lipa Summer School is a school on topics connected to logic in computer science. It is part of this grant. This is the second edition, the first one was in 2017 (there are videos). It will be held in Warsaw, June 25-28 2018. The school consists of 4 mini-courses given by:- Rajeev Alur (UPenn) Regular processing of data streams
- Matt Valeriote (McMaster) Finite algebras and connections with tree languages
- Igor Walukiewicz (Bordeaux) MSOL and higher-order computation
- Mikołaj Bojańczyk (Warsaw, organiser) Recognisable languages of graphs
Dates
May 15 End of registration with request for student accommodationJune 15 End of registration without request for student accommodation- June 25-28 School
Venue
The school will be held in (room C of the) Auditorium Maximum of the university of Warsaw, in the historical center of Warsaw. Here is the building:
Here is a map:
The school is part of the grant Lipa that has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 683080).
2015/2016
Algebraic Language Theory
The general theme is monoids instead of automata. We will go deep (e.g. on the structure of finite monoids) and wide (on "monoids" for infinite words etc.)
Lecture: Thursday 12:15 – 13:45 (room 3170) Exercise: Thursday 14:15 – 15:45 (room 3170)
I will use the notes from my previous course, but modified.
Advanced Topics in Automata (Języki, Automaty i Obliczenia 2)
This lecture is a choice of slightly more advanced topics from automata theory. The lecture is on Tuesdays, 12:15 in room 5070. The exercises are on Wednesdays, 16:15 in in room 5820, with Wojciech Czerwiński.- automata on infinite words: determinisation
- games of infinite duration: the Büchi-Landweber theorem
- weighted automata: decidable and undecidable problems
- distance automata: decidability of limitedness
- tree-walking automata: failure of determinisation
- transducers
- learning automata: the Angluin algorithm
- automata with infinite alphabets
- sets with atoms
2014/2015
Algebraic Language Theory
This course is about an alternative approach to regular languages, where one uses monoids or semigroups instead of automata. Lecture: Tuesdays 8:45-10:15 (room 5070) Exercises: Tuesdays 10:25-11:55 (room 5070)Języki i paradygmaty programowania
Laboratorium do wykładu Marcina Benke.2013/2014
2011/2012
2009/2010
2008/2009