Bridging Course Foundations of Informatics

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 2022/23. It is offered in March 2023 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

Schedule

TBA

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:

  • Regular Languages (TBA)
  • Context-Free Languages (TBA)

The following exam questions provide an orientation regarding the contents of the exam:

In addition, you may want to have a look at the Theory of Computation online course, in particular the following parts:

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]