Highlights of the Computational Complexity Certification Course by Brainmeasures

The Computational complexity certification course by Brainmeasures is a detailed course that discusses and explains all the main areas of this subject. Some of the major points of this course are mentioned below:

• Gives you an introduction of the basic complexity classes and modelling computation.
• Discusses NP and NP completeness and the class NP.
• Explains diagonalization and the time hierarchy and non-deterministic time hierarchy theorems.
• Discusses space complexity and space bounded computation.
• Explains the polynomial hierarchy and the alternations.
• Discusses about finer gradations and circuit classes.
• Explains randomized computation and probabilistic computation.
• Explains about interactive proofs and some variations.
• Explains about cryptography and computational security.
• Discusses about quantum computation and the various algorithms.
• Discusses about PCP theorem and the hardness of approximation.
• Explains about lower bounds for concrete computational models.
• Discusses communicational complexity.
• Discusses circuit lower bounds and complexity theory’s waterloo. Explains proof complexity with the help of some examples.
• Discusses about Algebraic computational models.
• Discusses advanced topics, complexity of counting.
• Explains the average case complexity with the help of Levin’s theory.
• Guides you about hardness amplification and error correcting.
• Explains about derandomization.
• Discusses pseudorandom constructions along with its expanders and extractors.
• Discusses the proofs of PCP theorems and the fourier transform technique.
• Explains why circuit lower bounds are difficult.
• Explains mathematical background in the appendix.