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**- 23 meetings- Meeting 01 : Mon, Jan 11, 11:00 am-11:50 am
- Meeting 02 : Wed, Jan 13, 09:00 am-09:50 am
- Meeting 03 : Thu, Jan 14, 01:00 pm-01:50 pm
- Meeting 04 : Mon, Jan 18, 11:00 am-11:50 am
- Meeting 05 : Tue, Jan 19, 10:00 pm-10:50 pm
- Meeting 06 : Wed, Jan 20, 09:00 am-09:50 am
- Meeting 07 : Wed, Jan 27, 09:00 am-09:50 am
- Meeting 08 : Thu, Jan 28, 01:00 pm-01:50 pm
- Meeting 09 : Mon, Feb 01, 11:00 am-11:50 am
- Meeting 10 : Tue, Feb 02, 10:00 pm-10:50 pm
- Meeting 11 : Wed, Feb 03, 09:00 am-09:50 am
- Meeting 12 : Thu, Feb 04, 01:00 pm-01:50 pm
- Meeting 13 : Thu, Feb 04, 02:00 pm-02:50 pm
- Meeting 14 : Mon, Feb 08, 11:00 am-11:50 am
- Meeting 15 : Tue, Feb 09, 10:00 pm-10:50 pm
- Meeting 16 : Thu, Feb 11, 01:00 pm-01:50 pm
- Meeting 17 : Mon, Feb 15, 11:00 am-11:50 am
- Meeting 18 : Tue, Feb 16, 10:00 pm-10:50 pm
- Meeting 19 : Wed, Feb 17, 09:00 am-09:50 am
- Meeting 20 : Wed, Feb 24, 09:00 am-09:50 am
- Meeting 21 : Thu, Feb 25, 01:00 pm-01:50 pm
- Meeting 22 : Mon, Feb 29, 11:00 am-11:50 am
- Meeting 23 : Tue, Mar 01, 10:00 pm-10:50 pm

Basic Admin data fixed. <br> Notion of Computation. A view from science and engineering sides. Algorithmic Data Processing and Mathematical Theorem proving. Ruler and Compass constructions. References Refer to class notes. Exercises Reading <a href="http://www.math.uiuc.edu/~rotman/ruler.pdf">Ruler and Compass Constructions.</a><br> <a href="http://www.trnicely.net/pentbug/pentbug.html">Intel FDIV bug</a> Basic Admin data fixed.

Notion of Computation. A view from science and engineering sides. Algorithmic Data Processing and Mathematical Theorem proving. Ruler and Compass constructions.References : Refer to class notes. Reading : Ruler and Compass Constructions.

Intel FDIV bugTA group allocation. Details of grading and activities of the course.<br> Formalizing Algorithmic Problem descriptions. Notion of an alphabet and a language. References Exercises Reading TA group allocation. Details of grading and activities of the course.

Formalizing Algorithmic Problem descriptions. Notion of an alphabet and a language.References : None Alphabets, Strings, Operations on Strings. Languages. Operations on Languages. Powering, Asterate. Problems vs Languages. References Lecture 2 in Kozen's Textbook. Exercises Reading Alphabets, Strings, Operations on Strings. Languages. Operations on Languages. Powering, Asterate. Problems vs Languages.References : Lecture 2 in Kozen's Textbook. Modelling a push-button switch. States, Transitions. Formal definition of a finite automata. Coffee Machine example. Language accepted by the FA. References Exercises Reading Modelling a push-button switch. States, Transitions. Formal definition of a finite automata. Coffee Machine example. Language accepted by the FA.References : None A mathematical proof that design of the push button switch indeed meets the user requirements. More examples of design and proof of correctness of finite automata. References The second example is from Lecture 3 in [K] Exercises Generalize the construction and proof to show that the following set S(p,k) can be accepted by a finite automaton. S(p,k) is the set of strings over the alphabet {0,1,2 ... p-1} which are p-ary representations of multiples of k (leading 0s are allowed). How many states does your automaton use? Reading A mathematical proof that design of the push button switch indeed meets the user requirements. More examples of design and proof of correctness of finite automata.References : The second example is from Lecture 3 in [K] Exercises : Generalize the construction and proof to show that the following set S(p,k) can be accepted by a finite automaton. S(p,k) is the set of strings over the alphabet {0,1,2 ... p-1} which are p-ary representations of multiples of k (leading 0s are allowed). How many states does your automaton use? Regular languages. Are all languages regular? Closure properties of the set of regular languages. Complementation. Product construction. References Lecture 3 in [K] Exercises Reading Regular languages. Are all languages regular? Closure properties of the set of regular languages. Complementation. Product construction.References : Lecture 3 in [K] 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 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 : None More examples of non-regularity. Abstraction from the proofs to a formal statement of pumping Lemma. View of the Game with the Demon. References Exercises Reading More examples of non-regularity. Abstraction from the proofs to a formal statement of pumping Lemma. View of the Game with the Demon.References : None Proof of the pumping Lemma. Applications. References Exercises Reading Proof of the pumping Lemma. Applications.References : None More example applications of the pumping lemma. Strengthened versions of the pumping lemma. References Exercises Reading More example applications of the pumping lemma. Strengthened versions of the pumping lemma.References : None Collapsing states in a finite automaton. Minimization. References Exercises Reading Collapsing states in a finite automaton. Minimization.References : None Quotient construction and its correctness. <br> Marking Algorithm and its correctness. References Exercises Reading Quotient construction and its correctness.

Marking Algorithm and its correctness.References : None Viewing automaton as a string classifier. Myhill-Nerode relations. From Automata to Myhill-Nerode relations. Using Myhill-Nerode theorem to show non-regularity. References Exercises Reading Viewing automaton as a string classifier. Myhill-Nerode relations. From Automata to Myhill-Nerode relations. Using Myhill-Nerode theorem to show non-regularity.References : None More examples of using Myhill-Nerode theorem to show non-regularity. From Myhill-Nerode relations to Automaton. Using Myhill-Nerode theorem to show optimality of automaton. References Exercises Reading More examples of using Myhill-Nerode theorem to show non-regularity. From Myhill-Nerode relations to Automaton. Using Myhill-Nerode theorem to show optimality of automaton.References : None Coarsest and Finest Myhill-Neorde Relations with respect to the same language. A characterization for the coarsest Myhill-Nerode relation. Connections to Minimal Automata. References Exercises Reading Coarsest and Finest Myhill-Neorde Relations with respect to the same language. A characterization for the coarsest Myhill-Nerode relation. Connections to Minimal Automata.References : None The Two-way Finite Automaton (2way FAs). An example language where 2-way FA design is easier. The formal model of computation. Accepting, Rejecting and Looping. References Exercises Reading The Two-way Finite Automaton (2way FAs). An example language where 2-way FA design is easier. The formal model of computation. Accepting, Rejecting and Looping.References : None Proof that 2-way finite automaton accepts only regular languages. A nontrivial use of Myhill-Nerode theorem. References Exercises Reading Proof that 2-way finite automaton accepts only regular languages. A nontrivial use of Myhill-Nerode theorem.References : None Non-deterministic automaton, motivation, formal definition, examples, and the view as a subset automaton. References Exercises Reading Non-deterministic automaton, motivation, formal definition, examples, and the view as a subset automaton.References : None Formal proof of the subset construction. A "guess+verify view" of non-determinism. Epsilon-transitions and applying subset construction in that case. 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.References : None TBA References Exercises Reading TBAReferences : None Expressing languages using expressions. References Exercises Reading Expressing languages using expressions.References : None From Finite Automaton to Regular Expressions. Minimal set of operations for regular expressions. References Exercises Reading From Finite Automaton to Regular Expressions. Minimal set of operations for regular expressions.References : None Closure of Regular Languages under Homomorphisms and image of homomorphisms. The Hamming Distance Language is regular for a fixed distance case. References Exercises Reading Closure of Regular Languages under Homomorphisms and image of homomorphisms. The Hamming Distance Language is regular for a fixed distance case.References : None **Theme 2 : Grammars & Context-free Languages**- 13 meetings- Meeting 24 : Wed, Mar 02, 09:00 am-09:50 am
- Meeting 25 : Thu, Mar 03, 01:00 pm-01:50 pm
- Meeting 26 : Mon, Mar 07, 11:00 am-11:50 am
- Meeting 27 : Tue, Mar 08, 10:00 pm-10:50 pm
- Meeting 28 : Thu, Mar 10, 01:00 pm-01:50 pm
- Meeting 29 : Mon, Mar 14, 11:00 am-11:50 am
- Meeting 30 : Tue, Mar 15, 10:00 pm-10:50 pm
- Meeting 31 : Wed, Mar 16, 09:00 am-09:50 am
- Meeting 32 : Mon, Mar 21, 11:00 am-11:50 am
- Meeting 33 : Tue, Mar 22, 10:00 pm-10:50 pm
- Meeting 34 : Wed, Mar 23, 09:00 am-09:50 am
- Meeting 35 : Mon, Mar 28, 11:00 am-11:50 am
- Meeting 36 : Wed, Mar 30, 09:00 am-09:50 am

Grammars and Context-free languages. Introduction, motivation and formal definition of a grammar. Derivation, sentential forms and language generated by a grammar. References Exercises Reading Grammars and Context-free languages. Introduction, motivation and formal definition of a grammar. Derivation, sentential forms and language generated by a grammar.References : None Example context-free grammars and languages. Example derivations. The PAREN language and its importance. A grammar for PAREN. Exercises on grammar writing. References Exercises Reading Example context-free grammars and languages. Example derivations. The PAREN language and its importance. A grammar for PAREN. Exercises on grammar writing.References : None Showing that the grammar for PAREN is indeed correct. A proof that Regular Languages are context-free. References Exercises Reading Showing that the grammar for PAREN is indeed correct. A proof that Regular Languages are context-free.References : None Linear grammars and right-linearity. Regular languages are exactly same as right-linear grammars. References Exercises Reading Linear grammars and right-linearity. Regular languages are exactly same as right-linear grammars.References : None Four questions on CFLs. Non-context-freeness? Membership Testing? Closure Properties? Machine models?<br> A key tool : Chomsky Normal Form for CFLs. References Exercises Reading Four questions on CFLs. Non-context-freeness? Membership Testing? Closure Properties? Machine models?

A key tool : Chomsky Normal Form for CFLs.References : None Conversion of any CFL to Chomsky Normal Form. Eliminating epsilon and unit productions. Correctness proof for the procedure. Examples. References Exercises Reading Conversion of any CFL to Chomsky Normal Form. Eliminating epsilon and unit productions. Correctness proof for the procedure. Examples.References : None Derivations, Parse Trees and an intuition leading towards pumping lemma. References Exercises Reading Derivations, Parse Trees and an intuition leading towards pumping lemma.References : None Pumping Lemma for CFLs. Proof and two applications. References Exercises Reading Pumping Lemma for CFLs. Proof and two applications.References : None CYK Algorithm for CFLs References Exercises Reading CYK Algorithm for CFLsReferences : None Towards a machine model for CFLs. Greibach Normal Form. References Exercises Reading Towards a machine model for CFLs. Greibach Normal Form.References : None From a CFL in GNF to a PDA. References Exercises Reading From a CFL in GNF to a PDA.References : None From a PDA to a 1-state PDA. From a 1-state PDA to a CFG. References Exercises Reading From a PDA to a 1-state PDA. From a 1-state PDA to a CFG.References : None Finishing up the proof. Interesting Computational Problems about CFLs. References Exercises Reading Finishing up the proof. Interesting Computational Problems about CFLs.References : None **Theme 3 : Turing Machines & Computability**- 10 meetings- Meeting 37 : Thu, Mar 31, 01:00 pm-01:50 pm
- Meeting 38 : Mon, Apr 04, 11:00 am-11:50 am
- Meeting 39 : Tue, Apr 05, 10:00 pm-10:50 pm
- Meeting 40 : Thu, Apr 07, 01:00 pm-01:50 pm
- Meeting 41 : Mon, Apr 11, 11:00 am-11:50 am
- Meeting 42 : Tue, Apr 12, 10:00 pm-10:50 pm
- Meeting 43 : Wed, Apr 13, 09:00 am-09:50 am
- Meeting 44 : Mon, Apr 18, 11:00 am-11:50 am
- Meeting 45 : Tue, Apr 19, 10:00 pm-10:50 pm
- Meeting 46 : Mon, Apr 25, 11:00 am-11:50 am

To Be Announced References Exercises Reading To Be AnnouncedReferences : None To Be Announced References Exercises Reading To Be AnnouncedReferences : None To Be Announced References Exercises Reading To Be AnnouncedReferences : None To Be Announced References Exercises Reading To Be AnnouncedReferences : None To Be Announced References Exercises Reading To Be AnnouncedReferences : None To Be Announced References Exercises Reading To Be AnnouncedReferences : None To Be Announced References Exercises Reading To Be AnnouncedReferences : None To Be Announced References Exercises Reading To Be AnnouncedReferences : None To Be Announced References Exercises Reading To Be AnnouncedReferences : None To Be Announced References Exercises Reading To Be AnnouncedReferences : None **Theme 4 : Evaluation & Tutorial Meetings**- 12 meetings- Meeting 47 : Thu, Jan 21, 01:00 pm-01:50 pm
- Meeting 48 : Wed, Feb 10, 09:00 am-09:50 am
- Meeting 49 : Thu, Feb 18, 01:00 pm-01:50 pm
- Meeting 50 : Tue, Feb 23, 10:00 pm-10:50 pm
- Meeting 51 : Thu, Mar 03, 02:00 pm-02:50 pm
- Meeting 52 : Wed, Mar 09, 09:00 am-09:50 am
- Meeting 53 : Thu, Mar 17, 01:00 pm-01:50 pm
- Meeting 54 : Tue, Mar 29, 08:00 am-08:50 am
- Meeting 55 : Wed, Apr 06, 09:00 am-09:50 am
- Meeting 56 : Thu, Apr 21, 01:00 pm-01:50 pm
- Meeting 57 : Tue, Apr 26, 10:00 pm-10:50 pm
- Meeting 58 : Tue, May 03, 09:00 am-12:00 pm

DoT 01 References Exercises Reading DoT 01References : None ShoT 01 References Exercises Reading ShoT 01References : None DoT 02 References Exercises Reading DoT 02References : None Quiz - I References Exercises Reading Quiz - IReferences : None DoT 03 References Exercises Reading DoT 03References : None ShoT 02 References Exercises Reading ShoT 02References : None DoT 03-a References Exercises Reading DoT 03-aReferences : None Quiz - II References Exercises Reading Quiz - IIReferences : None ShoT 03 References Exercises Reading ShoT 03References : None DoT 04 References Exercises Reading DoT 04References : None ShoT 04 References Exercises Reading ShoT 04References : None Endsem References Exercises Reading EndsemReferences : None