Course description:
The course has very little connection to programming, you don't need to
know how to write programs. It is about the theoretical questions that
arise from computers. Consider it more mathematics than computer
science. However, nowadays every mathematician should know something
about complexity theory.
Topics covered:
-
Finite automata, regular and non-regular languages, pumping lemma.
- Context-Free languages.
- Turing Machines, universal Turing machines.
The existence of universal Turing machines.
- Recursive functions. Recursive, recursively enumerable languages.
- Algorithmic decidability,
Halting problem and other undecidable problems.
- Storage and time, general theorems on space and time complexity
- Non-deterministic Turing-machines. NP and co-NP.
- Cook's theorem: SAT is NP-complete.
Other NP-complete problems.
- Kolmogorov-complexity of sequences.