Complexity and Computability
bldg. 10, room 0A182,
(716) 475-5193, email@example.com
office hours TR 8-10pm
Tuesday/Thursday, 6-8pm, 12-3105
Books and Other Reading
- M. Sipser,
Introduction to the Theory of Computation, PWS Publ, 1997
- C. Papadimitriou,
Computational Complexity, Addison-Wesley 1994
- M. Garey and D. Johnson,
Computers and intractability : a guide to the theory of NP-completeness,
W. H. Freeman 1979 (suggested reference).
- D. Hofstadter,
Gödel, Escher, Bach : an eternal golden braid,
New York Basic Books 1979 (suggested reading).
- E. Nagel and J.R. Newman,
New York University Press 1958 (suggested reading).
- Journal articles.
ICSS 380 or ICSG 700.
General knowledge of programming. Some background in combinatorics and
discrete mathematics are desirable.
Introduction to the complexity and computability theories.
Overview of basic complexity classes, with special focus on
NP-theory related problems. Study of problems complete in
NP and PSPACE. Church-Turing thesis. Undecidability of
chosen classical problems. Some advanced topics in
computability, like degrees of unsolvability, recursion
theorem or Gödel's incompleteness theorem, are included.
Turing machines based computability
- Church-Turing Thesis
- Hilbert's problems
- Diagonalization method
- (Non)-decidable-solvable-computable-recursive problems
- Halting problem
- Undecidability by reductions
- Program equivalence
- Printable = recursively enumerable (r.e.)
- Problems in formal languages
Selected advanced topics
- Beyond r.e.
- Recursion theorem
- Creative sets
- Arithmetical hierarchy
- Complexity of proving theorems
- Gödel's incompleteness theorem
- Models of computation
- Computational problems, algorithms, complexity
- P versus NP
- Reducibility and completeness
- Satisfiability problem
- Chosen graph problems
- Traveling salesman
- Garey-Johnson catalog
- NP, coNP, primality testing
- PSPACE, pebbling and games
- Logarithmic space, path problem
- Interactive proof systems
- Time and space hierarchy
- Polynomial hierarchy
- Beyond PSPACE
- Other miscellaneous classes