Circuit Complexity Theory

By Prof. Raghunath Tewari   |   IIT Kanpur
Learners enrolled: 75
This is a course on Boolean Circuit Complexity. In this course we study the Boolean circuit model of computation. We prove upper and lower bounds on circuit resources such as depth and size. The course is entirely mathematical, and a good level of mathematical maturity is essential. Prior knowledge of discrete mathematics, probability and basic algebra are prerequisites for this course. The course is intended for students who wish to pursue research in theoretical computer science.

INTENDED AUDIENCE: Computer Science advanced undergraduate and postgraduate student interested in theoretical computer science

PREREQUISITES: Basic undergraduate course in Theory of Computation and Algorithms. Undergraduate algebra and discrete mathematics.
Course Status : Upcoming
Course Type : Elective
Duration : 12 weeks
Start Date : 23 Jan 2023
End Date : 14 Apr 2023
Exam Date : 29 Apr 2023 IST
Enrollment Ends : 30 Jan 2023
Category :
  • Computer Science and Engineering
Credit Points : 3
Level : Undergraduate/Postgraduate

Page Visits

Course layout

Week 1: Boolean functions, circuits, formula, Shannon's Theorem, Riordon-Shannon Theorem
Week 2: Khrapchenko's Theorem and its applications, Nechiporuk's Theorem, Random Restriction
Week 3: Subbotovskaya's lower bound on formula size, Andreev function, Polynomial sized monotone formula for majority (Valiant's Theorem)
Week 4: Complexity of basic arithmetic operations - addition, multiplication, division
Week 5: Bounded depth circuits, the complexity classes, NC, AC and TC. Division, powering and iterated products in NC (Beame-Cook-Hoover Theorem)
Week 6: Uniform model of computation - Turing machines and its relationship with circuits
Week 7: Method of approximations, monotone lower bound on cliques of small size
Week 8: Monotone lower bound on cliques of arbitrary size
Week 9: Razborov-Smolensky lower bound for parity
Week 10: Lower bound for parity using Hastad's Switching Lemma
Week 11: Communication complexity and its relation to circuit complexity, Karchmer-Wigderson Theorem
Week 12: Recent advances in circuit lower bounds

Books and references


Instructor bio

Prof. Raghunath Tewari

IIT Kanpur
Raghunath Tewari is an Associate Professor in the department of Computer Science and Engineering at IIT Kanpur. His research interests lie in the areas of computational complexity theory, algorithms and graph theory.

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: 29 April 2023 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.


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 Kanpur .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

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