The plan/details for each meeting is/are recorded here in the chronological order.
- Missing lectures Aug 1,2,3,5
- Lecture 00 : Mon, Aug 8, 9-9:50am - Overview & Administrative trivia
- Lecture 01 : Tue, Aug 9, 8-8:50am - Historical aspects of
computability and complexity theory.
Review & More : Automata and Languages.
(18 meetings - 17 Lectures, 1 Quiz)
- (Upcoming) Lecture 02 : Wed, Aug 10, 12-12:50pm :
Review : Languages, Problems, Encodings. Notion of a state,
finite state automata. Closure properties of regular languages.
- (Upcoming) Lecture 03 : Fri, Aug 12, 11-11:50am :
Nondeterminism, Subset construction, Regular expressions
- (Upcoming) Lecture 04 : Tue, Aug 16, 8-8:50am :
Combinatorial Construction of Autamata from the regular
expression and vice versa. Kleene Algebra, Matrices over Kleene
Algebra
- (Upcoming) Lecture 05 : Wed, Aug 17, 12-12:50pm :
From Automata to Kleene expressions
- (Upcoming) Lecture 06 : Fri, Aug 19, 11-11:50am :
Pumping Lemma, Applications and its variations
- (Upcoming) Lecture 07 : Sat, Aug 20, 1:30pm-2:20pm (for Aug 1) :
Myhill-Nerode relations and theorem, and Proof of the stronger pumping lemma
- (Upcoming) Lecture 08 : Sat, Aug 20, 2:30pm-3:30pm (for Aug 2) :
Is input mechanism of a DFA a restriction? Two-way finite
Automata and acceptance conditions.
- Missing lectures : Aug 22.
- (Upcoming) Lecture 09 : Tue, Aug 23, 8-8:50am :
2-way DFA's and regular sets, intuitive argument, crossing
functions
- Missing lectures : Aug 24.
- (Upcoming) Lecture 10 : Fri, Aug 26, 11-11:50am :
Myhill-Nerode relations for languages accepted by 2-DFA
- (Upcoming) Lecture 11 : Sun, Aug 28, 2pm-2:50pm (for Aug 3) :
Homorphisms, Properties of regular sets under homomorphisms,
applications
- (Upcoming) Lecture 12 : Sun, Aug 28, 3am-3:50pm (for Aug 5) :
In memory a restriction?
Adding a stack, push down automaton.
Quick review of grammars and
Normal forms
- (Upcoming) Lecture 13 : Mon, Aug 29, 9-9:50am :
Pumping Lemma for CFLs, and an application
- (Upcoming) Lecture 14 : Tue, Aug 30, 8-8:50am :
Review of closure properties of CFLs
- (Upcoming) Lecture 15 : Fri, Sep 2, 11-11:50am :
Structure of CFLs - I : Chomsky-Schutzenberger Theorem
- (Upcoming) Lecture 16 : Mon, Sep 5, 9-9:50am :
Structure of CFLs - II : Semi-linear sets and Regular Languages
- QUIZ - I - (Upcoming) Lecture 17 : Tue, Sep 6, 8-8:50am :
Material : Theme 1 - Regular Languages, CFLs
- (Upcoming) Lecture 18 : Wed, Sep 7, 12-12:50pm :
Proof of Parikh's theorem
- Missing lecture - Sep 9.
- (Upcoming) Lecture 19 : Mon, Sep 12, 9-9:50am :
Computability (19 meetings - 17 lectures, 2 Tutorials)
- (Upcoming) Lecture 20 : Tue, Sep 13, 10am-10:50am (rescheduled 8am slot lecture) :
Hilbert's program, different attempts to capture the notion of an effective procedure, Church-Turing thesis, TMs as finite automata with infinite memory, formal model, halting, acceptance.
- (Upcoming) Lecture 21 : Wed, Sep 14, 12-12:50pm :
Configurations, Language accepted by TMs, Decidability and Semi-decidability, Complementation.
Equivalent models to TMs - two-way infinite TMs, two stack PDAs, multitape TMs
- Tutorial 01 : Wed, Sep 14, 4pm-5pm :
Topics : Quiz-I solutions discussion
- (Upcoming) Lecture 22 : Fri, Sep 16, 11-11:50am :
Enumeration Machines, Enumerable languages,
Encodings of Turing machines. Universal Turing Machines
- (Upcoming) Lecture 23 : Sun, Sep 18, 2pm-2:50pm (for Aug 22) :
Recap, Cantors Diagonalization argument, Undecidability of the Halting Problem (HP)
- (Upcoming) Lecture 24 : Sun, Sep 18, 3pm-3:50am (for Aug 24) :
Undecidability of the MP - Membership Problem, Notion of Reductions
- (Upcoming) Lecture 25 : Mon, Sep 19, 9-9:50am :
Musings on reductions, and properties towards Rice's theorem, the REG language
- (Upcoming) Lecture 26 : Tue, Sep 20, 8-8:50am :
Infinitely many undecidable sets
Rice's theorem I - All nontrivial properties of semidecidable sets are undecidable
- (Upcoming) Lecture 27 : Wed, Sep 21, 12-12:50pm :
Landscape of undecidable sets, Semidecidable and Co-semidecidable sets
Rice's theorem II - No non-monotone property of semidecidable sets is semi-decidable.
Applications to semi-decidability question of of REG and its complement
- Tutorial 02 : Wed, Sep 21, 4pm-5pm :
Topics : TM Model, Undecidability, Reductions
- (Upcoming) Lecture 28 : Fri, Sep 23, 11-11:50am :
Proof details of Rice's theorem II. Implications of Rice's Theorem.
- Special Lecture : Sep 25, 9am - 12pm
Language of Numbers, Peano's Arithmetic
Godel's First Incompleteness theorem and a proof using computability.
- (Upcoming) Lecture 29 : Mon, Sep 26, 9-9:50am :
More on reductions : Characterising Semidecidable sets by Halting Problem
- (Upcoming) Lecture 30 : Tue, Sep 27, 8-8:50am :
Statement and consequences of Freidberg-Muchnik theorem,
Infinite strict chain of problems between Halting Problem and any decidable set.
- (Upcoming) Lecture 31 : Wed, Sep 28, 12-12:50pm :
Relative Computation, Oracle Turing Machines
- Special Lecture : Sep 28, 6:15pm - 8:15pm
Godel's Proof of First and Second Incompleteness theorems.
- (Upcoming) Lecture 32 : Mon, Oct 3, 9-9:50am :
Landscape outside semi-decidables : A heirarchy of languages.
A way to use it. Existential Predicate characterisation of Semi-decidable languages
- (Upcoming) Lecture 33 : Tue, Oct 4, 8-8:50am :
Quantified Predicate characterisation of the arithmetic Heirarchy
- (Upcoming) Lecture 34 : Wed, Oct 5, 12-12:50pm :
- Missing Lecture : Oct 7th.
- (Upcoming) Lecture 35 : Mon, Oct 10, 9-9:50am :
Applications, Positioning the languages FIN, TOTAL, EMPTY in the heirarchy
- (Upcoming) Lecture 36 : Tue, Oct 11, 8-8:50am :
Completeness in the arithmetic heirarchy
- (Upcoming) Lecture 37 : Wed, Oct 12, 12-12:50pm :
Resources of computation, Blum's axioms, Examples and non-examples of resources
- Tutorial 03 : Sat, Oct 15, 2pm-4pm :
Topics : PS1 & PS2 solutions discussion
- (Upcoming) Lecture 38 : Fri, Oct 14, 11-11:50am :
Structure in the world of decidable languages. g-decidable languages
- (Upcoming) Lecture 39 : Mon, Oct 17, 9-9:50am :
A language outside the g-decidables : Hartmanis-Stearns Theorem
- QUIZ - II - (Upcoming) Lecture 40 : Tue, Oct 18, 8-8:50am :
Time & Space Complexity (15 meetings - 13 Lectures, 1 Tutorial, 1 Quiz)
- (Upcoming) Lecture 41 : Wed, Oct 19, 12-12:50pm :
Time, Space, Heirarchy theorems, Hennie-Stearns tape reduction theorem (statement).
- (Upcoming) Lecture 42 : Fri, Oct 21, 11-11:50am :
Measuring Resources in terms of input length, Specialising the theory
DTIME(t(n)), DSPACE(s(n))
- (Upcoming) Lecture 43 : Sun, Oct 23, 2pm-2:50pm (for Sep 9) :
What is the notion of a best algorithm? Speed up for Palindrome Language
- (Upcoming) Lecture 44 : Sun, Oct 23, 3pm-3:50am (for Oct 7) :
Blum's Speedup Theorem (statement) and ideas of the proof.
- (Upcoming) Lecture 45 : Mon, Oct 24, 9-9:50am :
Tape compression theorem, Space Complexity classes
- (Upcoming) Lecture 46 : Tue, Oct 25, 8-8:50am :
Linear Speed up theorem, Time complexity classes
- (Upcoming) Lecture 47 : Fri, Oct 28, 11-11:50am :
Crossing sequence arguments - Quadratic time lower bounds for Palindrome language
- (Upcoming) Lecture 48 : Mon, Oct 31, 9-9:50am :
Complexity Classes P, EXP, PSPACE. Separations due to heirarchy theorem.
Notion of efficiency in time, space. Robustness requirements
- (Upcoming) Lecture 49 : Wed, Nov 2, 12-12:50pm :
Simulations, Padding Arguments
- Tutorial 04 : Wed, Nov 2, 4pm-5pm :
Topics : From computability to complexity : example problems
- (Upcoming) Lecture 50 : Fri, Nov 4, 11-11:50am :
Non-determinism, NP, Simulations and Containments
- (Upcoming) Lecture 51 : Tue, Nov 8, 8-8:50am :
CLIQUE problem, EXP algorithm, PSPACE algorith, NP algorithm,
Guess+Verify characterisation of NP
- (Upcoming) Lecture 52 : Wed, Nov 9, 12-12:50pm :
INDSET problem, NP algorithm, connection between CLIQUE and INDSET.
Reductions, Completeness, Bounded Halting Problem is NP-complete
- (Upcoming) Lecture 53 : Fri, Nov 11, 11-11:50am :
Cook-Levin Theorem - SAT is NP-complete
- (Upcoming) Lecture 54 : Sat, Nov 12, 2pm-2:50pm :
CNF SAT, 3-SAT, INDSET, CLIQUE .... world of NP-completeness.
- (Upcoming) Lecture 55 : Sat, Nov 12, 3pm-3:50am :
Graph Isomorphism Problem. Ladner's Theorem (statement).
Warmup - review of Padding Technique : Relating NEXP vs EXP and NP vs P
- (Upcoming) Lecture 56 : Mon, Nov 14, 9-9:50am :
Impagliazzo's Proof of Ladner's Theorem
- (Upcoming) Lecture 57 : Tue, Nov 15, 8-8:50am :
Turing reductions, Examples, Oracle Machines, Polynomial Hierarchy, PSPACE upper bound
- (Upcoming) Lecture 58 : Wed, Nov 16, 12-12:50pm :
Non-deterministic Space Complexity : NPSPACE, NL : NSPACE(s) is contained in DTIME(2^s).
Savitch's Theorem : NSPACE(s) is contained in DSPACE(s^2), and hence PSPACE=NPSPACE
- (Upcoming) Lecture 59 : Fri, Nov 18, 11-11:50am :
Review, Next-steps, Teacher-Course-Feedback
- Tutorial 05 : Sat, Nov 19, 2pm-4pm :
Topics : PS3 & PS4 discussions
- ENDSEM Exam: (Upcoming) Lecture 60 : Tue, Nov 22, 9am-12pm :
Statistics : 60 meetings - 57 lectures, 2 Quizzes, and 1 Endsem
