Week 3: Formal Languages and Processes
This page collects the relevant material of the third week of the Foundations of Informatics Bridging Course in Winter Semester 2021/22. It is held from March 7 to 11, 2022, as an online course, and covers the following topics:
- Part A: Regular Languages
- Introduction to Formal Languages
- Deterministic and Nondeterministic Finite Automata
- Regular Expressions and Languages
- Closure and Decidability Properties
- Part C: Context-Free Languages
- Context-Free Grammars and Languages
- Relation to Regular Languages
- Pushdown Automata
- Closure and Decidability Properties
The planned schedule is as follows (details to follow):
- Monday, March 7:
- 09:00-09:30: Kick-off meeting via Zoom
- Slides of kick-off
- Remainder of day: Self-paced learning by means of videos
- Tuesday, March 8:
- Wednesday, March 9:
- Thursday, March 10:
- Friday, March 11:
Objectives
After passing this part of the course, participants are expected to have acquired the following skills:
- Regular Languages:
- to give the basic definitions of finite automata and regular expressions;
- to construct a finite automaton or a regular expression from a given language description;
- to translate a regular expression into an equivalent finite automaton;
- to compute the set of reachable states of a finite automaton with respect to a given input word;
- to remove ε-transitions from a finite automaton;
- to apply the powerset construction to turn a nondeterministic finite automaton into a deterministic one; and
- to minimise a given deterministic finite automaton.
- Context-Free Languages:
- to give the basic definitions of context-free grammars and pushdown automata;
- to construct a context-free grammar or a pushdown automaton from a given language description;
- to turn a given context-free grammar into Chomsky normal form;
- to apply the CYK algorithm to decide the word problem for a context-free grammar;
- to apply the marking algorithm to decide the emptiness problem for a context-free grammar; and
- to translate a context-free grammar into an equivalent pushdown automaton.
Additional Material
A Moodle course with quizzes (requires registration):
The video lessons are based on the following slides:
The following exam questions provide an orientation regarding the contents of the exam:
- Exam questions (.zip archive)
In addition, you may want to have a look at the Theory of Computation online course, in particular the following parts:
- Deterministic Finite State Machines: Introduction
- Deterministic Finite State Machines: Examples
- Operations on Regular Languages
- Nondeterministic Finite State Machines: Introduction
- Nondeterministic Finite State Machines: Formal Definition
- Equivalence of Deterministic and Nondeterministic FSMs
- Closure of Regular Operations
- Regular Expressions
- Equivalence of Regular Expressions and Regular Languages
- Context-Free Grammars and Languages
- An Example Context-Free Language and Grammar
- Chomsky Normal Form
- Pushdown Automata
Moreover, the following textbooks provide additional information:
- J.E. Hopcroft, R. Motwani, J.D. Ullmann: Introduction to Automata Theory, Languages, and Computation, 2nd ed., Addison-Wesley, 2001
- A. Asteroth, C. Baier: Theoretische Informatik, Pearson Studium, 2002 [in German]