# Computational Complexity

By Prof. Subrahmanyam Kalyanasundaram   |   IIT Hyderabad
Learners enrolled: 906
This course is an introduction to the area of computational complexity theory. We will see different models of computations and computational complexity classes. The computational models measure various different aspects of computation, like time, space, randomness, number of gates, amount of communication etc. The complexity classes classify different computational problems depending on their easiness or hardness as per these different models. We will also see how these complexity classes are related to each other. Many of the results are extremely interesting and use several interesting ideas.

INTENDED AUDIENCE  :  Students of Computer Science discipline. This could be BTech students who are interested in Theory or MTech/PhD students.
PREREQUISITES  :  Theory of Computation.
Summary
 Course Status : Completed Course Type : Elective Duration : 12 weeks Category : Computer Science and Engineering Foundations of Computing Credit Points : 3 Level : Postgraduate Start Date : 26 Jul 2021 End Date : 15 Oct 2021 Enrollment Ends : 09 Aug 2021 Exam Date : 24 Oct 2021 IST

Note: This exam date is subjected to change based on seat availability. You can check final exam date on your hall ticket.

### Course layout

Week-1: Introduction to the course, Review of NP Completeness, P vs NP, Cook-Levin Theorem
Week-2: Time Hierarchy Theorem, Polynomial Hierarchy, Introduction to Space Complexity
Week-3: Savitch’s Theorem, NL-Completeness, NL = coNL
Week-4: PSPACE Completeness, Space Hierarchy Theorem, Baker-Gill-Solovay Theorem
Week-5: Randomized Complexity Classes, BPP is in polynomial hierarchy
Week-6: Nonuniform computation, Circuit Complexity
Week-7: Parity not in AC^0
Week-8: Karp-Lipton Theorem, Adleman’s Theorem, Polynomial Identity Testing, Isolation Lemma, Perfect Matching is in RNC^2
Week-9: #P and #P Completeness. Permanent is #P Complete.
Week-10: Valiant Vazirani Theorem and Toda’s Theorem
Week-11: Communication Complexity, Monotone depth lower bound for matching
Week-12: Interactive Proofs.

### Books and references

1. Computational Complexity, by Christos Papadimitriou
2. Computational Complexity: A Modern Approach, by Sanjeev Arora and Boaz Barak.
3. Introduction to the Theory of Computation by Michael Sipser

### Prof. Subrahmanyam Kalyanasundaram

Subrahmanyam Kalyanasundaram is an Associate Professor at the Department of Computer Science and Engineering, IIT Hyderabad. He did his Masters from Dept of ECE in IISc. After which, he did his Masters in Mathematics and Phd in Algorithms, Combinatorics and Optimization from Georgia Tech. He has been at the Department of Computer Science and Engineering, IIT Hyderabad since 2011. He is interested in almost all areas of theoretical computer science, and has most recently been working on combinatorics, graph theory and graph algorithms of late.

### Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 24 October 2021 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Hyderabad .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team