The student is acquainted with important notions and algorithms
regarding formal languages, automata, grammars, compilers, computability
This course addresses foundational questions in computer science, such
- "What is a (programming) language?",
- "How can languages be recognised by computers (automata)",
- "Which problems can be solved using a class of automata?",
- "How much time and memory does solving a problem require?".
The course is divided into the following parts: automata & languages and
The first part, on automata and languages, deals with the concepts of
formal language, grammar, and automaton. Two types of languages are
covered: regular and context-free languages. Regular languages are used,
e.g., in search queries, in the form of regular expressions.
Context-free languages are suitable to describe programming languages.
The automata-theoretic counterparts here are finite automata and the
more powerful pushdown automata. Pumping lemmas are discussed to
determine whether a language is regular or context-free. With each type
of language a class of grammars is associated: left-linear and
context-free grammars. Parsing algorithms are presented for context-free
languages, to determine whether a string is in the language.
In the second part of the course, on computability theory, the central
question is "Which computations can be performed on a computer?". To
reason about this question, Turing machines are introduced, as well the
Church-Turing thesis, along with examples of undecidable problems: the
halting problem and the Post correspondence problem. It is shown how
undecidability of new problems can be shown by reduction from a known
undecidable problem. Important complexity classes from the complexity
hierarchy are discussed, notably P, NP, and NP-complete, together with
the corresponding reduction arguments.
4 hours per week lectures; 4 hours per week exercise classes
Weekly homework exercises (which can earn up to 0.5 bonus points). The
homework is mandatory to qualify for the exam.
Peter Linz, An Introduction to Formal Languages and Automata, Jones &
Bartlett, 4th or 5th edition