Two similar courses will be run simultaneously, one for UG students and another for PG students.
UG Course Credits: 4 Prerequisites: Algorithms, Discrete Maths, Theory of Computing
Postconditions: Upon successful completion of the course, the student will gain the following:
 knowledge of different models of computation and their relationships
 ability to bound resource usage (e.g., time, space, circuit size, depth) required for problems under different models of computation
 ability to place a problem in the hierarchy of computational complexity classes
 ability to show separations, collapses of classes and prove completeness of problems
 understand the major questions (e.g., P =? NP) and their role in other fields of computer science

PG Course
Credits: 4Prerequisites: Algorithms, Discrete Maths, Theory of Computing, ProbabilityPostconditions: Upon successful completion of the course, the student will gain the following: knowledge of different models of computation and their relationships
 ability to bound resource usage (e.g., time, space, circuit size, depth) required for problems under different models of computation
 ability to place a problem in the hierarchy of computational complexity classes
 ability to show separations, collapses of classes and prove completeness of problems
 understand the major questions (e.g., P =? NP) and their role in other fields of computer science
 develop knowledge of randomized complexity classes and ability to perform randomized reductions

DescriptionComputational problems can be studied from the point of view of computational resources (e.g., running time) required to solve them – this forms the notional of computational difficulty. Apart from the nature of the problem, the difficulty also depends on the underlying model of computation. Problems can be related to each other based on their resource usage, and problems with similar difficulty can be grouped together to form a classification of computational problems into complexity classes.
Computational complexity is about studying the above concepts, and is especially concerned with giving precise upper and lower bound on the amount of resources required to solve certain problems. This has had a profound impact on current algorithm design and cryptography, and still sees applications in areas outside of theoretical computer science.  InstructionLectures will follow a mixture of regular lectures and flippedclassroom model. Hence, maturity in logic and reasoning is mandatory. The course will start where a standard course on Theory of Computation ends, hence it is strongly advisable that students are comfortable and strong in TOC.
Book  [S] Michael Sipser, “Introduction to the Theory of Computation”
 [AB] Sanjeev Arora and Boaz Barak. “Complexity Theory: A Modern Approach”
Evaluation: 75% exams, 25% coursework and homework
 40% final exam
 30% midsem
 5% quiz
 25% homework
Tentative schedule
Week  Topics  Chapter  1  Turing machine definition, variants  S3 AB1 Lec01 Lec02
 2  Turing machine contd. UTM, simulation of TMs
 S3 AB1 Lec03 Lec04
 3  Palindrome lower bound. Linear speedup, Defining and relating complexity classes
 Lec05 Lec06 Lec07
 4  Inclusions and separations: Tally language, padding technique, time hierarchy theorem  S9.1 AB2 AB3 Lec08 Lec09
 5  Reductions, hardness and complete problems
 S7 AB2 Lec10 Lec11
 6  Relativization, BGS
 S8 AB3 Lec12 Lec13
 7  Space complexity
 S8 AB4 Lec1415
 8  Space complexity: PSPACE, L, NL
 S8 AB4 Lec16 Lec17
 9  Polytime hierarchy, alternation  S10, AB5 Lec19 Lec20
 10  Circuit complexity
 S9 AB6 Lec21 Lec22 Lec2324
 11  Nonuniform complexity
 Lec2526

 Adv topics
(PG) Probabilistic complexity classes  S10 
Advanced topics: counting complexity, interactive proofs, communication complexity 