Computational Complexity Theory

In this course we study mathematical techniques that enable us to show the power and limitations of various computational models. We consider these models by putting restrictions on the resources that the model can use and study the class of problems that are solvable by these models. We also compare the various classes that are thus obtained and try to give relations between them.
INTENDED AUDIENCE :Advanced undergraduate and postgraduate studentsPREREQUISITES : Design and Analysis of Algorithms, Theory of ComputationINDUSTRIES SUPPORT :None

COURSE LAYOUT

Week 1:NP CompletenessWeek 2:Hierarchy Theorems, Space ComplexityWeek 3:Space Complexity (contd)Week 4:Polynomial Hierarchy
Week 5:Circuit ComplexityWeek 6:Randomized ComplexityWeek 7:Valiant Vazirani TheoremWeek 8:Toda’s Theorem, Complexity of Permanent function
Week 9:Interactive ProofsWeek 10:Interactive Proofs (contd)Week 11:Circuit Lower BoundsWeek 12:Communication Complexity, PCP Theorem