Formal Languages and Logic, Fall 2018 (CO21-320352)
Jacobs University Bremen, Fall 2018, Herbert Jaeger
Class sessions: Tuesdays 9:45-11:00 (Lecture Hall Res. 1), Thursdays 11:15-12:30 (West Hall 8)
Office hours:No regular office hours. If I'm in my office and you want to see me, knock and enter and I will have time. If you want to make sure that I am in, drop me an email for fixing an appointment.
Topics: Formal languages, discrete automata, first-order logic. This course gives an introduction to the most basic themes of theoretical computer science. Formal languages and discrete automata are the fundaments of programming languages and their parsing and compiling. First-order logic is the basis of artificial intelligence, program verification and advanced data base systems.
Lecture notes: self-contained, complete set of lecture notes. Last update Oct 17 Updated Oct 17, 2018 (typos, font conversion errors, updated URLs, nothing crucial)
Further helpful documents:
- A collection of exercises and exams with solutions from 2003 (pdf)
- A collection of exercises and exams with solutions from 2004 (pdf)
- A collection of exercises and exams with solutions from 2005 (pdf)
- The midterm and final exam questions with solutions, 2006 (pdf)
- The final exam from 2010 with solutions (multiple choice format) (pdf)
Additional reading: a condensed intro to RDF, written by Jan Wilken Dörrie. To be enjoyed at the end of the lecture as this concerns a marriage between logic and grammars, of central importance for "semantic web" techologies.
Course culture. The online lecture notes are a fully self-contained, textbook-style, detailed text. All exam questions are based solely on what is in the lecture notes. Thus, a student could perfectly pass this course by just home-studying the lecture notes, tuning his/her skills on the weekly homeworks, sit in the exams, and be done without ever seeing me. Ooops. I do want to see my students... Easy: I make classroom attendance mandatory. Ooops again - mandatory boredom? Solution: (i) mandatory classroom presence, (ii) mandatory pre-reading of the lecture note portion of the day, (iii) in class I will only briefly rehearse the pre-read lecture note material, making sure that everybody has a good grasp of it, and then (iv) I will spend most of the classroom time telling you stuff that is related to the lecture note material, but outside of it -- stuff you will not find in typical lecture notes: historical background, applications, connections of computer science to other sciences, tricky problems and open questions, math minitutorials, and more. This "extra" stuff will, I hope, make attendance worth its while, although it is not exam-relevant. You will, I hope very much, be amazed how deeply the technical material of this lecture is connected to realities outside (and underneath) CS.
Grading and exams: Grading and exams: The final course grade will be composed from homeworks (15%), presence sheets (10%), and quizzes (45%) and a final exam (30%). There will be three miniquizzes (written in class, 30 minutes), the best two of which will be counted (worst will be dropped). All quizzes and the final exam are open book. Each quiz or exam yields a maximum of 100 points.
Miniquiz makeup rules: if a miniquiz is missed without excuse, it will be graded with 0 points. A makeup will be offered for medically excused miniquizzes according to the Jacobs rules (specifically, the medical excuse must be announced to me before the miniquiz). Non-medical excuses can be accepted on a case-by-case basis.
References (optional! the online lecture notes suffice)
- Hopcroft, John E., Motwani, Rajeev, and Ullman, Jeffrey: Introduction to Automata Theory, 2nd (Addison-Wesley). The standard textbook for most parts of this lecture, except for the logic part. IRC: QA267 .H56 2001
-
Schoening, Uwe: Logic for Computer Scientists (Progress in Computer Science and Applied Logic, Vol 8), (Birkhauser). The book contains what its title suggests. IRC: QA9 .S363 1989
Schedule (this will be filled in synchrony with reality as we go along)
| Sep 4 | Introduction |
| Sep 6 | Basic notation. The concept of a formal language. Two kinds of infinities, one of them kind, the other a brute. (= Lecture notes Section 2) Exercise sheet 1 |
| Sep 11 | Deterministic Finite Automata (DFAs) and Nondeterministic Finite Automata (NFAs). Reading: LN Section 3 up to (including) Example 3.3. |
| Sep 13 | Equivalence of DFAs and NFAs. Reading: LN Section 3 up to (excluding) Def. 3.7. Exercise sheet 2 Solutions to exercise sheet 1 |
| Sep 18 | no class (illness) |
| Sep 20 | epsilon-NFAs, Moore and Mealy machines. Reading: LN Section 3.1 complete Solutions to exercise sheet 2 |
| Sep 25 | Regular expressions and their equivalence with DFAs. Reading: LN Section 3.2 (we skip the material in 3.3) Slides: a zoo of finite-state system models (and for the ambitious ones: here is the full dynamical systems course slideset) |
| Sep 27 | Pumping Lemma and closure properties of regular languages. Reading: LN Sections 3.4, 3.5. Exercise sheet 3 (extended version, now covering 2 weeks) |
| Oct 2 | First miniquiz (in CNLH!) Myhill-Nerode theorem. No reading, fyi: material covered will be the theorem statement and its proof, found in the beginning of LN Section 3.6. |
| Oct 4 | Minimization of DFAs. Decision properties of regular languages (lecturer of the day: Xu He) Reading: LN Section 3.6 to end Exercise sheet 4 Solutions to exercise sheet 3 |
| Oct 9 | Grammars: basic definitions. Reading: LN Sections 4.1 |
| Oct 11 | Ambiguity. Grammars for regular languages. Reading: LN Sections 4.2, 4.3 Exercise sheet 5 Solutions to exercise sheet 4 |
| Oct 16 | Pushdown automata. Reading: no reading expected. Class will be held by Xu He. |
| Oct 18 | The magic of XML. Reading: LN Sections 4.4 Solutions to exercise sheet 5 Exercise sheet 6 |
| Oct 25 | Finishing PDAs. Chomsky Normal Form. Reading: LN Sections 4.5, 4.6 Exercise sheet 7 |
| Oct 30 | Closure properties of CFLs and the CYK algorithm. Reading: LN Section 4.8 Solutions to exercise sheet 6 |
| Nov 1 | Grammars: final remarks. Other kinds of Grammars. Chomsky hierarchy. Reading: LN Section 5 Solutions to exercise sheet 7 Exercise sheet 8 (a very lightweight one) |
| Nov 6 | Second miniquiz (venue: CNLH) Introduction to first-order logic. No reading. |
| Nov 8 | Syntax of FOL. Reading: LN Section 7.1 Solutions to exercise sheet 8 Exercise sheet 9 |
| Nov 13 | Formalizing pieces of the world in FOL - training session. No reading |
| Nov 15 | Semantics of FOL 1: S-structures. Reading: LN Section 7.2 up to (excluding) Def. 7.6 Solutions to exercise sheet 9 Exercise sheet 10 |
| Nov 20 | Semantics of FOL 2: S-interpretations. Model relation and logical entailment Reading: LN Section 7.2 complete. |
| Nov 22 | Another training session: examples of S-structures, model relation, and entailment. No reading. Solutions to exercise sheet 10 Exercise sheet 11 |
| Nov 27 | Entailment - concluding remarks. The sequent calculus: intro. Reading: LN Section 8 (up to and including the list of rules). |
| Nov 29 | Derived rules. Derivations in the sequent calculus. Reading: LN Section 8, complete. Exercise sheet 12, with solutions, for self-study (do not return) |
| Dec 4 | Third miniquiz (venue: CNLH). Followed by time for online course evaluation. A zoo of logics - informal overview. No reading. |
| Dec 6 | Completeness of FOL. Concluding remarks. Reading: LN Section 9 up to (including) proof sketch of completeness theorem. |
| Dec 15 | Final exam: 9:00-11:00, SCC Hall 3 |