Meetings

Click on the theme item for the meeting plan for that theme.Click on the meeting item for references, exercises, and additional reading related to it.

**Theme 1 : Finite Automata & Regular Languages**- 15 meetings- Meeting 01 : Wed, Jan 15, 09:00 am-09:50 am
- Meeting 02 : Thu, Jan 16, 01:00 pm-01:50 pm
- Ruler and Compass Constructions
- Lecture 1 of Kozen's Book.
- Meeting 03 : Mon, Jan 20, 11:00 am-11:50 am
- Is Sigma^* countably infinite?
- Is the number of languages over Sigma countably infinite?
- Meeting 04 : Tue, Jan 21, 10:00 am-10:50 am
- Meeting 05 : Wed, Jan 22, 09:00 am-09:50 am
- Meeting 06 : Thu, Jan 23, 10:00 am-10:50 pm
- Meeting 07 : Mon, Jan 27, 11:00 am-11:50 am
- Meeting 08 : Tue, Jan 28, 10:00 am-10:50 am
- Meeting 09 : Wed, Jan 29, 09:00 am-09:50 am
- Meeting 10 : Thu, Jan 30, 01:00 pm-01:50 pm
- 2nd half of Lecture 12 of Kozen's Textbook.
- Myhill-Nerode Relations (notes by Jayalal)
- On Ultimate Periodicity - Kozen
- Combinatorics on Words - A tutorial - see Chapter 3 in particular
- Automata, Boolean Matrices, and Ultimate Periodicity
- Meeting 11 : Mon, Feb 03, 11:00 am-11:50 am
- For a given language A, can there be two non-equivalent Myhill-Nerode relations respecting A.
- Can the reverse direction of Myhill-Nerode theorem hold?
- Myhill-Nerode Relations (Notes by Jayalal)
- Try proving that {a^p : p is a prime} is not regular by using the weak Myhill-Nerode Theorem.
- Meeting 12 : Tue, Feb 04, 10:00 am-10:50 am
- Meeting 13 : Wed, Feb 05, 09:00 am-09:50 am
- Meeting 14 : Mon, Feb 10, 11:00 am-11:50 am
- Lecture 17 of Kozen's Textbook.
- Meeting 15 : Tue, Feb 11, 10:00 am-10:50 am

Administrative Announcements <br> Discussion : Why this course? <br> Science side : What is computation? The generality of the concept. Quest for understanding limits. <br> Engineering side : Building complicated systems from simple ones. Notion of proof of correctness. The importance via an example. <br> Simple systems first. Coffee machine, Push button switch. What problem does Push button switch "solve"? What language does it "understand"? It does distinguish between odd number of pushes and even number of pushes. References It was an introductory lecture. The instructor did not follow any class notes. Exercises Attempt on formalizations of the questions raised in this lecture. Reading <a href="http://www.trnicely.net/pentbug/pentbug.html">Pentium FDIV flaw</a> Administrative Announcements

Discussion : Why this course?

Science side : What is computation? The generality of the concept. Quest for understanding limits.

Engineering side : Building complicated systems from simple ones. Notion of proof of correctness. The importance via an example.

Simple systems first. Coffee machine, Push button switch. What problem does Push button switch "solve"? What language does it "understand"? It does distinguish between odd number of pushes and even number of pushes.References : It was an introductory lecture. The instructor did not follow any class notes. Exercises : Attempt on formalizations of the questions raised in this lecture. Reading : Pentium FDIV flaw An example study - The Ruler and Compass Construction. Possibilities and Impossibilities. Challenges and excitement. A comparison to what computability would aim to argue.<br> Back to the formalization of language of the push button switch. Alphabet, Strings, concatenation. References <ul> <li><a href="http://en.wikipedia.org/wiki/Compass-and-straightedge_construction">Ruler and Compass Constructions</a></li> <li>Lecture 1 of Kozen's Book.</li> </ul> Exercises Try out to find a construction using Ruler and Compass alone to construct a regular pentagon (given only the unit length edge initially).<br> Thought exercise : Why Ruler and Compass? What if we disallow the compass also? What if we add a divider? <br> Can Sigma^* contain strings of infinite length? Reading <a href="http://web.science.mq.edu.au/~chris/geometry/CHAP09%20Ruler%20and%20Compass%20Constructions.pdf">More on the compass and straight edge</a> An example study - The Ruler and Compass Construction. Possibilities and Impossibilities. Challenges and excitement. A comparison to what computability would aim to argue.

Back to the formalization of language of the push button switch. Alphabet, Strings, concatenation.References : Exercises : Try out to find a construction using Ruler and Compass alone to construct a regular pentagon (given only the unit length edge initially).

Thought exercise : Why Ruler and Compass? What if we disallow the compass also? What if we add a divider?

Can Sigma^* contain strings of infinite length?Reading : More on the compass and straight edge Languages. Language Recognition vs Problem Solving. Encoding of problem input instances. References Exercises <ul> <li>Is Sigma^* countably infinite?</li> <li>Is the number of languages over Sigma countably infinite?</li> </ul> Reading Languages. Language Recognition vs Problem Solving. Encoding of problem input instances.References : None Exercises : Modeling the push button switch. Observations and the notion of a state. Transition diagram. An abstract machine model of a finite state machine. Example of a coffee machine. Modeling the machine and the transition diagram. <br> Formal set up : Finite state machine as 5-tuple. Transition function. References Lecture 3 of [Kozen] Book. Exercises How do we formalize, "Machine run on an input x reaches a particular state" when we understand the one-step run of the machine? Reading Modeling the push button switch. Observations and the notion of a state. Transition diagram. An abstract machine model of a finite state machine. Example of a coffee machine. Modeling the machine and the transition diagram.

Formal set up : Finite state machine as 5-tuple. Transition function.References : Lecture 3 of [Kozen] Book. Exercises : How do we formalize, "Machine run on an input x reaches a particular state" when we understand the one-step run of the machine? Extended Transition Functions. Language accepted by a finite automata. Example automata. Proof technique of induction. References Exercises Reading Extended Transition Functions. Language accepted by a finite automata. Example automata. Proof technique of induction.References : None Simple constructions of Automata. Regular languages. Closure under complementation, intersection. Product Construction. References Lecture 3 of [Kozen]. Some examples are not directly from the textbook. Exercises Reading Simple constructions of Automata. Regular languages. Closure under complementation, intersection. Product Construction.References : Lecture 3 of [Kozen]. Some examples are not directly from the textbook. A full proof for an example - the divisibility by three of the binary number. Closure Properties of Regular Languages. (Set theoretic operations). References Lecture 4 in Kozen's Textbook Exercises Consider a language A that is regular and is accepted with an automaton with exactly one final state. Can you find an automaton for the reversal of A (the set of strings each of which is a reversal of some string in A)? In your answer have you crucially used that the automaton for A has only one final state? If so, attempt to do it without that assumption. Reading A full proof for an example - the divisibility by three of the binary number. Closure Properties of Regular Languages. (Set theoretic operations).References : Lecture 4 in Kozen's Textbook Exercises : Consider a language A that is regular and is accepted with an automaton with exactly one final state. Can you find an automaton for the reversal of A (the set of strings each of which is a reversal of some string in A)? In your answer have you crucially used that the automaton for A has only one final state? If so, attempt to do it without that assumption. Limitations of Finite automaton. Two example languages which cannot be accepted by finite automaton. Proof that they are not regular - demonstrations of how formally exploit the "finiteness" of the number of states. References Lecture 11 of Kozen's Textbook. Exercises Reading Limitations of Finite automaton. Two example languages which cannot be accepted by finite automaton. Proof that they are not regular - demonstrations of how formally exploit the "finiteness" of the number of states.References : Lecture 11 of Kozen's Textbook. The formal statement of pumping Lemma. View of the Game with the Demon. Example proofs where Lemma is applied. References Exercises Reading The formal statement of pumping Lemma. View of the Game with the Demon. Example proofs where Lemma is applied.References : None Ultimate Periodicity and Regularity for unary languages. <br> Viewing Automata as classifiers. Defining an equivalence relation on Sigma^* using the extended transition function. More properties of this equivalence relation. References <ul> <li>2nd half of Lecture 12 of Kozen's Textbook.</li> <li><a href="http://www.cse.iitm.ac.in/~jayalal/teaching/CS2200/myhill-nerode.pdf">Myhill-Nerode Relations</a> (notes by Jayalal)</li> </ul> Exercises Reading <ul> <li><a href="http://www.cs.cornell.edu/~kozen/papers/up.pdf">On Ultimate Periodicity</a> - Kozen</li> <li><a href="http://www-igm.univ-mlv.fr/~ejc2003/part4.ps">Combinatorics on Words</a> - A tutorial - see Chapter 3 in particular</li> <li><a href="http://www.ai.uga.edu/ftplib/zhang-papers/dfa-matrix.ps.gz">Automata, Boolean Matrices, and Ultimate Periodicity</a></li> </ul> Ultimate Periodicity and Regularity for unary languages.

Viewing Automata as classifiers. Defining an equivalence relation on Sigma^* using the extended transition function. More properties of this equivalence relation.References : Reading : Myhill-Nerode Relations. From Automata to Myhill-Nerode relations. (Weak) Myhill-Nerode theorem. Using them to show that {a^nb^n} cannot be regular? Two questions (raised in class by students during "Neighbor Time") <ul> <li>For a given language A, can there be two non-equivalent Myhill-Nerode relations respecting A.</li> <li>Can the reverse direction of Myhill-Nerode theorem hold?</li> </ul> Yes, (stronger form of) Myhill-Nerode Theorem. Construction of Automata from Myhill-Nerode relations. Proof of correctness deferred to the next lecture. References <ul> <li><a href="http://www.cse.iitm.ac.in/~jayalal/teaching/CS2200/myhill-nerode.pdf">Myhill-Nerode Relations</a> (Notes by Jayalal)</li> </ul> Exercises <ul> <li>Try proving that {a^p : p is a prime} is not regular by using the weak Myhill-Nerode Theorem.</li> </ul> Reading Myhill-Nerode Relations. From Automata to Myhill-Nerode relations. (Weak) Myhill-Nerode theorem. Using them to show that {a^nb^n} cannot be regular? Two questions (raised in class by students during "Neighbor Time")References : Exercises : Proof of correctness of the automata constructed from any MN relation. Coarsest and Finest Myhill-Neorde Relations with respect to the same language. A characterization for the coarsest Myhill-Nerode relation. Minimal Automata. References Exercises Reading Proof of correctness of the automata constructed from any MN relation. Coarsest and Finest Myhill-Neorde Relations with respect to the same language. A characterization for the coarsest Myhill-Nerode relation. Minimal Automata.References : None Minimization Algorithm for Finite Automata. Example. Correctness Proof. Termination Argument. More examples. References Lecture on "Miniminization of Finite Automata" in Kozen's textbook. Exercises Reading Minimization Algorithm for Finite Automata. Example. Correctness Proof. Termination Argument. More examples.References : Lecture on "Miniminization of Finite Automata" in Kozen's textbook. Beyond Finite Automaton. Questioning the model. The Two-way Finite Automaton (2way FAs). An example language where 2-way FA design is easier. The motivating question - can it accept non-regular sets? The formal model of computation. Translating the intuitive model to formalism - the restrictions on the transition function. Accepting, Rejecting and Looping. References <ul> <li>Lecture 17 of Kozen's Textbook.</li> </ul> Exercises Reading Beyond Finite Automaton. Questioning the model. The Two-way Finite Automaton (2way FAs). An example language where 2-way FA design is easier. The motivating question - can it accept non-regular sets? The formal model of computation. Translating the intuitive model to formalism - the restrictions on the transition function. Accepting, Rejecting and Looping.References : Configurations and languages accepted by 2-way FAs. Using Myhill-Nerode relations to show that 2-way FAs accept only regular sets. References Exercises Reading Configurations and languages accepted by 2-way FAs. Using Myhill-Nerode relations to show that 2-way FAs accept only regular sets.References : None **Theme 2 : Non-determinism & Regular Expressions**- 9 meetings- Meeting 16 : Wed, Feb 12, 09:00 am-09:50 am
- Meeting 17 : Thu, Feb 13, 01:00 pm-01:50 pm
- Meeting 18 : Mon, Feb 17, 11:00 am-11:50 am
- Meeting 19 : Tue, Feb 18, 10:00 am-10:50 am
- Given a pattern and a string x how do we check whether the string "matches" the pattern?
- Can patterns express any set of strings that is not regular?
- Given two patterns how do we check whether they match the same set of strings.
- Are there redundant operators in our pattern system? Patterns which has only concatenation, + and Kleene *.
- Meeting 20 : Wed, Feb 19, 09:00 am-09:50 am
- Meeting 21 : Thu, Feb 20, 01:00 pm-01:50 pm
- Meeting 22 : Mon, Feb 24, 11:00 am-11:50 am
- Meeting 23 : Tue, Feb 25, 10:00 am-10:50 am
- Meeting 24 : Thu, Feb 27, 01:00 pm-01:50 pm

Back to the coffee machine example - the "faulty coffee machine". Motivating non-determinism. A new computational model. Example Automaton. References Exercises Reading Back to the coffee machine example - the "faulty coffee machine". Motivating non-determinism. A new computational model. Example Automaton.References : None More examples. A formal treatment for non-deterministic finite Automata and acceptance conditions. Subset construction (intuition). Formal proofs. References Exercises Reading More examples. A formal treatment for non-deterministic finite Automata and acceptance conditions. Subset construction (intuition). Formal proofs.References : None Formal proof of the subset construction. A "guess+verify view" of non-determinism. Epsilon-transitions and applying subset construction in that case. More closure properties of regular languages. References Exercises Reading Formal proof of the subset construction. A "guess+verify view" of non-determinism. Epsilon-transitions and applying subset construction in that case. More closure properties of regular languages.References : None Patterns and languages that match patterns. Patterns as a recursive definition - syntax and semantics. Four natural questions (raised in class by students during the neighbor time). <ul> <li>Given a pattern and a string x how do we check whether the string "matches" the pattern?</li> <li>Can patterns express any set of strings that is not regular?</li> <li>Given two patterns how do we check whether they match the same set of strings.</li> <li>Are there redundant operators in our pattern system? Patterns which has only concatenation, + and Kleene *.</li> </ul> References Exercises Reading Patterns and languages that match patterns. Patterns as a recursive definition - syntax and semantics. Four natural questions (raised in class by students during the neighbor time).References : None Answer to Question 2 : From patterns to Automata. Any set of strings that matches with a given pattern has to be regular. The inductive construction and proof of its correctness from the closure properties of regular languages. References Exercises Reading Answer to Question 2 : From patterns to Automata. Any set of strings that matches with a given pattern has to be regular. The inductive construction and proof of its correctness from the closure properties of regular languages.References : None Regular expressions. Patterns which has only concatenation, + and Kleene *. <br>Answer to Question 2 : From Automata to Regular Expressions. The recursive construction. Examples. References Exercises Reading Regular expressions. Patterns which has only concatenation, + and Kleene *.

Answer to Question 2 : From Automata to Regular Expressions. The recursive construction. Examples.References : None Simplification of regular expressions. Algebraic rules and equivalences. Examples. <br> Alphabet renaming in regular languages. Homomorphisms and definition of image and pre-image of a homomorphism. Closure property questions about regular languages. References Exercises Reading Simplification of regular expressions. Algebraic rules and equivalences. Examples.

Alphabet renaming in regular languages. Homomorphisms and definition of image and pre-image of a homomorphism. Closure property questions about regular languages.References : None Closure of Regular Languages under Homomorphisms and image of homomorphisms. References Exercises Reading Closure of Regular Languages under Homomorphisms and image of homomorphisms.References : None A nontrivial application of homomorphisms. The Hamming Distance Language is regular for a fixed distance case. <br> A second application : ultimate periodicity of the set of lengths of strings in a regular language. References Exercises Reading A nontrivial application of homomorphisms. The Hamming Distance Language is regular for a fixed distance case.

A second application : ultimate periodicity of the set of lengths of strings in a regular language.References : None **Theme 3 : Grammars & Context-Free Languages**- 16 meetings- Meeting 25 : Mon, Mar 03, 11:00 am-11:50 am
- Meeting 26 : Tue, Mar 04, 10:00 am-10:50 am
- Meeting 27 : Wed, Mar 05, 09:00 am-09:50 am
- Meeting 28 : Thu, Mar 06, 01:00 pm-01:50 pm
- Meeting 29 : Mon, Mar 10, 11:00 am-11:50 am
- Meeting 30 : Tue, Mar 11, 10:00 am-10:50 am
- Meeting 31 : Wed, Mar 12, 09:00 am-09:50 am
- Meeting 32 : Wed, Mar 19, 09:00 am-09:50 am
- Meeting 33 : Thu, Mar 20, 01:00 pm-01:50 pm
- Meeting 34 : Mon, Mar 24, 11:00 am-11:50 am
- Meeting 35 : Tue, Mar 25, 10:00 am-10:50 am
- Meeting 36 : Wed, Mar 26, 09:00 am-09:50 am
- Meeting 37 : Tue, Apr 01, 10:00 am-10:50 am
- Meeting 38 : Thu, Apr 03, 01:00 pm-01:50 pm
- Meeting 39 : Mon, Apr 07, 11:00 am-11:50 am
- Meeting 40 : Wed, Apr 09, 09:00 am-09:50 am

Language view. Grammar rules. Programming languages. Grammar rules for a subset of C language. Application of the idea to parsing. Example. Derivation of a string (informalview). Context-free property. Formalisation. References Exercises Reading Language view. Grammar rules. Programming languages. Grammar rules for a subset of C language. Application of the idea to parsing. Example. Derivation of a string (informalview). Context-free property. Formalisation.References : None Formal definition of a context-free grammar. Sentential forms. Derivation in one step. Derivation in arbitrary number of steps. Language generated by a grammar. Example. Balanced parenthesis and it's grammar. Complete formal proof that the grammar is correct. References Exercises Reading Formal definition of a context-free grammar. Sentential forms. Derivation in one step. Derivation in arbitrary number of steps. Language generated by a grammar. Example. Balanced parenthesis and it's grammar. Complete formal proof that the grammar is correct.References : None Context-free Languages, Unrestricted Grammars, Context-Sensitive Languages, Examples, Chomsky-Shutzenberger Hierarchy. Regular languages are also CFLs. Observations about the grammar that we obtained. Linear CFLs. Right-Linear CFLs. References Notes sent to the course mailing list. Exercises Reading Context-free Languages, Unrestricted Grammars, Context-Sensitive Languages, Examples, Chomsky-Shutzenberger Hierarchy. Regular languages are also CFLs. Observations about the grammar that we obtained. Linear CFLs. Right-Linear CFLs.References : Notes sent to the course mailing list. Example of the grammar construction from Automata. The converse of the theorem. From Right-Linear CFLs to Regular languages. <br> A discussion on why we would care much about CFLs in the Chomsky hierarchy. <br> Normal forms of Right Linear Grammars. Normal forms of CFGs. The statement of a useful normal form for CFGs. References Exercises Reading Example of the grammar construction from Automata. The converse of the theorem. From Right-Linear CFLs to Regular languages.

A discussion on why we would care much about CFLs in the Chomsky hierarchy.

Normal forms of Right Linear Grammars. Normal forms of CFGs. The statement of a useful normal form for CFGs.References : None Chomsky Normal Forms. Unit Productions and Epsilon productions. Eliminating them. Correctness of the algorithm. References Exercises Reading Chomsky Normal Forms. Unit Productions and Epsilon productions. Eliminating them. Correctness of the algorithm.References : None More Examples for converting CFGs to CNF form. References Exercises Reading More Examples for converting CFGs to CNF form.References : None Parse Trees. Yield of Parse tree. Parse tree of CNF grammars. Observations about the binary tree. Pumping Lemma for Context-free Languages - statement and proof. References Exercises Reading Parse Trees. Yield of Parse tree. Parse tree of CNF grammars. Observations about the binary tree. Pumping Lemma for Context-free Languages - statement and proof.References : None Applications of Pumping Lemma for CFLs. Examples. References Exercises Reading Applications of Pumping Lemma for CFLs. Examples.References : None Closure Properties of CFLs. Intersection with regular languages. References Exercises Reading Closure Properties of CFLs. Intersection with regular languages.References : None Examples where pumping Lemma is not applicable. Ogden's Lemma. Example application to show non-context-freeness. References Notes sent across. Exercises Reading Examples where pumping Lemma is not applicable. Ogden's Lemma. Example application to show non-context-freeness.References : Notes sent across. Ambiguity of CFGs, Inherent Ambiguity of CFLs, Applying Ogden's Lemma for proving inherent ambiguity of some CFLs. References Exercises Reading Ambiguity of CFGs, Inherent Ambiguity of CFLs, Applying Ogden's Lemma for proving inherent ambiguity of some CFLs.References : None Membership Testing Algorithm for CFLs. Cock-Younger-Kasami Algorithm. References Exercises Reading Membership Testing Algorithm for CFLs. Cock-Younger-Kasami Algorithm.References : None Machine Model. Non-deterministic Push-down Automaton. Acceptance Conditions. Finite State vs Empty Stack. References Exercises Reading Machine Model. Non-deterministic Push-down Automaton. Acceptance Conditions. Finite State vs Empty Stack.References : None From PDAs to CFGs. Construction and proof. References Exercises Reading From PDAs to CFGs. Construction and proof.References : None From CFGs to PDAs, GNF form for CFGs. References Exercises Reading From CFGs to PDAs, GNF form for CFGs.References : None Converting a CFL to GNF form. Converting a PDA to a PDA with only one state. Deterministic PDAs. References <a href="www.iitg.ernet.in/gkd/ma513/oct/oct18/note.pdf">Notes</a> Exercises Reading Extra reading : Deterministic CFLs Converting a CFL to GNF form. Converting a PDA to a PDA with only one state. Deterministic PDAs.References : Notes Reading : Extra reading : Deterministic CFLs **Theme 4 : Turing Machines & Computability**- 9 meetings- Meeting 41 : Thu, Apr 10, 10:00 am-10:50 am
- Meeting 42 : Thu, Apr 10, 01:00 pm-01:50 pm
- Meeting 43 : Tue, Apr 15, 10:00 am-10:50 am
- Meeting 44 : Wed, Apr 16, 11:00 am-11:50 am
- Meeting 45 : Mon, Apr 21, 11:00 am-11:50 am
- Meeting 46 : Tue, Apr 22, 10:00 am-10:50 am
- Meeting 47 : Wed, Apr 23, 09:00 am-09:50 am
- Meeting 48 : Tue, Apr 29, 10:00 am-10:50 am
- Meeting 49 : Tue, Apr 29, 11:00 am-11:50 am

Formal definition, Example of TM accepting a non-context-free language. Example Problems. References Exercises Reading Formal definition, Example of TM accepting a non-context-free language. Example Problems.References : None Effective computability. Introduction to TMs, Historical perspectives. Church-Turing thesis. References Exercises Reading Effective computability. Introduction to TMs, Historical perspectives. Church-Turing thesis.References : None Configurations, and acceptance. Language Accepted, Halting and Looping of Turing machine computations. Decidability and Semi-decidability. References Exercises Reading Configurations, and acceptance. Language Accepted, Halting and Looping of Turing machine computations. Decidability and Semi-decidability.References : None Equivalent models - Multiple Tapes, Two-way infinite tapes, Two stacks, Multiple heads. References Exercises Reading Equivalent models - Multiple Tapes, Two-way infinite tapes, Two stacks, Multiple heads.References : None Encoding Turing machines as strings, Universal Turing machine. Membership Problem(MP). Universal Turing machine semi-deciding MP. Halting Problem (HP), A TM semi-deciding HP. References Exercises Reading Encoding Turing machines as strings, Universal Turing machine. Membership Problem(MP). Universal Turing machine semi-deciding MP. Halting Problem (HP), A TM semi-deciding HP.References : None Undecidability of Halting Problem. Using total TM for MP to design a total TM for HP. Unudecidability of Membership problem. Finiteness checking of a given TM is also an undecidable problem - proof. References Exercises Reading Undecidability of Halting Problem. Using total TM for MP to design a total TM for HP. Unudecidability of Membership problem. Finiteness checking of a given TM is also an undecidable problem - proof.References : None Is Halting Problem hard because we dont in advance the input? Can we do some preprocessing of the input (and make HP_x decidable) if we knew it in advance before designing Total TM for HP. Negative answer - algorithm/TM. The language HP_101. References Exercises Reading Is Halting Problem hard because we dont in advance the input? Can we do some preprocessing of the input (and make HP_x decidable) if we knew it in advance before designing Total TM for HP. Negative answer - algorithm/TM. The language HP_101.References : None More Examples in the language of the reductions. HP to MP and MP to HP. Techniques of proving undecidability. References Exercises Reading More Examples in the language of the reductions. HP to MP and MP to HP. Techniques of proving undecidability.References : None (Optional Lecture) Journey within the decidable world. The notion of efficient computation. Computation resource - Time and Space as examples.Properties we expect from the notion of efficient computation. Class P. Verification vs Computation - NP vs P. References Exercises Reading (Optional Lecture) Journey within the decidable world. The notion of efficient computation. Computation resource - Time and Space as examples.Properties we expect from the notion of efficient computation. Class P. Verification vs Computation - NP vs P.References : None **Evaluation Meetings**- 7 meetings- Meeting 50 : Thu, Feb 06, 01:00 pm-01:50 pm
- Meeting 51 : Wed, Feb 26, 08:00 am-08:50 am
- Meeting 52 : Tue, Mar 18, 11:00 am-11:50 am
- Meeting 53 : Thu, Mar 27, 01:00 pm-01:50 pm
- Meeting 54 : Tue, Apr 08, 08:00 am-08:50 am
- Meeting 55 : Mon, Apr 28, 11:00 am-11:50 am
- Meeting 56 : Tue, May 06, 09:00 am-12:00 pm

ShoT 01<br> Syllabus : Lecture 1-13. References Exercises Reading ShoT 01

Syllabus : Lecture 1-13.References : None Quiz-I <br> Syllabus : Lectures 01 - 21 + half of Lecture 22. References Exercises Reading Quiz-I

Syllabus : Lectures 01 - 21 + half of Lecture 22.References : None ShoT 02: (Monday time table, although it is a Tuesday)<br> Syllabus : Lectures 23 - 32. References Exercises Reading ShoT 02: (Monday time table, although it is a Tuesday)

Syllabus : Lectures 23 - 32.References : None ShoT 03: <br> Syllabus : Lectures 32 - 37 References Exercises Reading ShoT 03:

Syllabus : Lectures 32 - 37References : None Quiz - II <br> Syllabus : Lectures 22-40 References Exercises Reading Quiz - II

Syllabus : Lectures 22-40References : None ShoT 04 <br> Lecture 42 - 49. References Exercises Reading ShoT 04

Lecture 42 - 49.References : None Endsemester Exam References Exercises Reading Endsemester ExamReferences : None **Theme 6 : Tutorial Meetings**- 5 meetings- Meeting 57 : Thu, Jan 30, 02:00 pm-03:00 pm
- Meeting 58 : Thu, Feb 20, 10:00 am-10:50 am
- Meeting 59 : Thu, Mar 06, 10:00 am-10:50 am
- Meeting 60 : Thu, Apr 03, 10:00 am-10:50 am
- Meeting 61 : Thu, Apr 17, 02:00 pm-03:00 pm

IDOT 01 (optional attendance) References Exercises Reading IDOT 01 (optional attendance)References : None IDOT 02 (optional attendance) References Exercises Reading IDOT 02 (optional attendance)References : None IDOT 03 (optional attendance) References Exercises Reading IDOT 03 (optional attendance)References : None IDOT 04 (Optional Attendance) References Exercises Reading IDOT 04 (Optional Attendance)References : None IDOT 05 (optional attendance) References Exercises Reading IDOT 05 (optional attendance)References : None