Automata and Complexity

 
Vakcode:
X_401049
Periode:
Periode 4
Credits:
6.0
Voertaal:
Engels
Faculteit:
Faculteit der Bètawetenschappen
Coördinator:
drs. J. Endrullis
Examinator:
drs. J. Endrullis
Docenten:
drs. J. Endrullis
Lesmethode(n):
Hoorcollege, Werkcollege
Niveau:
300

Doel vak

The student is acquainted with important notions and algorithms
regarding formal languages, automata, grammars, compilers, computability
and complexity.

This course addresses foundational questions in computer science, such
as:
- "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
computability theory.

Inhoud vak

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.

Onderwijsvorm

4 hours per week lectures; 4 hours per week exercise classes

Toetsvorm

Weekly homework exercises (which can earn up to 0.5 bonus points). The
homework is mandatory to qualify for the exam.

Written exam.

Literatuur

Peter Linz, An Introduction to Formal Languages and Automata, Jones &
Bartlett, 4th or 5th edition

Doelgroep

3CS

© Copyright Vrije Universiteit Amsterdam
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