CS2200 - Languages, Machines and Computation

Meetings  

• Theme 1 : Finite Automata & Regular Languages - 15 meetings

  • Meeting 01 : Wed, Jan 15, 09:00 am-09:50 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

  • Meeting 02 : Thu, Jan 16, 01:00 pm-01:50 pm

  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	:	Ruler and Compass Constructions Lecture 1 of Kozen's Book.
  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

  • Meeting 03 : Mon, Jan 20, 11:00 am-11:50 am

  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	:	Is Sigma^* countably infinite? Is the number of languages over Sigma countably infinite?

  • Meeting 04 : Tue, Jan 21, 10:00 am-10:50 am

  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?

  • Meeting 05 : Wed, Jan 22, 09:00 am-09:50 am

  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

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  None

  • Meeting 06 : Thu, Jan 23, 10:00 am-10:50 pm

  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

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  Lecture 3 of [Kozen]. Some examples are not directly from the textbook.

  • Meeting 07 : Mon, Jan 27, 11:00 am-11:50 am

  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.

  • Meeting 08 : Tue, Jan 28, 10:00 am-10:50 am

  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

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  Lecture 11 of Kozen's Textbook.

  • Meeting 09 : Wed, Jan 29, 09:00 am-09:50 am

  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

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  None

  • Meeting 10 : Thu, Jan 30, 01:00 pm-01:50 pm

  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	:	2nd half of Lecture 12 of Kozen's Textbook. Myhill-Nerode Relations (notes by Jayalal)
  Reading	:	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

  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")

  • 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?

  Yes, (stronger form of) Myhill-Nerode Theorem. Construction of Automata from Myhill-Nerode relations. Proof of correctness deferred to the next lecture.
  

  References	:	Myhill-Nerode Relations (Notes by Jayalal)
  Exercises	:	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

  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

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  None

  • Meeting 13 : Wed, Feb 05, 09:00 am-09:50 am

  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

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  Lecture on "Miniminization of Finite Automata" in Kozen's textbook.

  • Meeting 14 : Mon, Feb 10, 11:00 am-11:50 am

  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

  :

  Lecture 17 of Kozen's Textbook.

  • Meeting 15 : Tue, Feb 11, 10:00 am-10:50 am

  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

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  None

• Theme 2 : Non-determinism & Regular Expressions - 9 meetings

  • Meeting 16 : Wed, Feb 12, 09:00 am-09:50 am

  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

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  None

  • Meeting 17 : Thu, Feb 13, 01:00 pm-01:50 pm

  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

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  None

  • Meeting 18 : Mon, Feb 17, 11:00 am-11:50 am

  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

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  None

  • Meeting 19 : Tue, Feb 18, 10:00 am-10:50 am

  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).

  • 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 *.

  
  

  References

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  None

  • Meeting 20 : Wed, Feb 19, 09:00 am-09:50 am

  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

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  None

  • Meeting 21 : Thu, Feb 20, 01:00 pm-01:50 pm

  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

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  None

  • Meeting 22 : Mon, Feb 24, 11:00 am-11:50 am

  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

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  None

  • Meeting 23 : Tue, Feb 25, 10:00 am-10:50 am

  Closure of Regular Languages under Homomorphisms and image of homomorphisms.

  References
  Exercises
  Reading

  Closure of Regular Languages under Homomorphisms and image of homomorphisms.
  

  References

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  None

  • Meeting 24 : Thu, Feb 27, 01:00 pm-01:50 pm

  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

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  None

• Theme 3 : Grammars & Context-Free Languages - 16 meetings

  • Meeting 25 : Mon, Mar 03, 11:00 am-11:50 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

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  None

  • Meeting 26 : Tue, Mar 04, 10:00 am-10:50 am

  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

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  None

  • Meeting 27 : Wed, Mar 05, 09:00 am-09:50 am

  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.

  • Meeting 28 : Thu, Mar 06, 01:00 pm-01:50 pm

  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

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  None

  • Meeting 29 : Mon, Mar 10, 11:00 am-11:50 am

  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

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  None

  • Meeting 30 : Tue, Mar 11, 10:00 am-10:50 am

  More Examples for converting CFGs to CNF form.

  References
  Exercises
  Reading

  More Examples for converting CFGs to CNF form.
  

  References

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  None

  • Meeting 31 : Wed, Mar 12, 09:00 am-09:50 am

  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

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  None

  • Meeting 32 : Wed, Mar 19, 09:00 am-09:50 am

  Applications of Pumping Lemma for CFLs. Examples.

  References
  Exercises
  Reading

  Applications of Pumping Lemma for CFLs. Examples.
  

  References

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  None

  • Meeting 33 : Thu, Mar 20, 01:00 pm-01:50 pm

  Closure Properties of CFLs. Intersection with regular languages.

  References
  Exercises
  Reading

  Closure Properties of CFLs. Intersection with regular languages.
  

  References

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  None

  • Meeting 34 : Mon, Mar 24, 11:00 am-11:50 am

  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.

  • Meeting 35 : Tue, Mar 25, 10:00 am-10:50 am

  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

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  None

  • Meeting 36 : Wed, Mar 26, 09:00 am-09:50 am

  Membership Testing Algorithm for CFLs. Cock-Younger-Kasami Algorithm.

  References
  Exercises
  Reading

  Membership Testing Algorithm for CFLs. Cock-Younger-Kasami Algorithm.
  

  References

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  None

  • Meeting 37 : Tue, Apr 01, 10:00 am-10:50 am

  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

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  None

  • Meeting 38 : Thu, Apr 03, 01:00 pm-01:50 pm

  From PDAs to CFGs. Construction and proof.

  References
  Exercises
  Reading

  From PDAs to CFGs. Construction and proof.
  

  References

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  None

  • Meeting 39 : Mon, Apr 07, 11:00 am-11:50 am

  From CFGs to PDAs, GNF form for CFGs.

  References
  Exercises
  Reading

  From CFGs to PDAs, GNF form for CFGs.
  

  References

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  None

  • Meeting 40 : Wed, Apr 09, 09:00 am-09:50 am

  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

  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

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  None

  • Meeting 42 : Thu, Apr 10, 01:00 pm-01:50 pm

  Effective computability. Introduction to TMs, Historical perspectives. Church-Turing thesis.

  References
  Exercises
  Reading

  Effective computability. Introduction to TMs, Historical perspectives. Church-Turing thesis.
  

  References

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  None

  • Meeting 43 : Tue, Apr 15, 10:00 am-10:50 am

  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

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  None

  • Meeting 44 : Wed, Apr 16, 11:00 am-11:50 am

  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

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  None

  • Meeting 45 : Mon, Apr 21, 11:00 am-11:50 am

  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

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  None

  • Meeting 46 : Tue, Apr 22, 10:00 am-10:50 am

  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

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  None

  • Meeting 47 : Wed, Apr 23, 09:00 am-09:50 am

  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

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  None

  • Meeting 48 : Tue, Apr 29, 10:00 am-10:50 am

  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

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  None

  • Meeting 49 : Tue, Apr 29, 11:00 am-11:50 am

  (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

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  None

• Evaluation Meetings - 7 meetings

  • Meeting 50 : Thu, Feb 06, 01:00 pm-01:50 pm

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

  References
  Exercises
  Reading

  ShoT 01
  Syllabus : Lecture 1-13.
  

  References

  :

  None

  • Meeting 51 : Wed, Feb 26, 08:00 am-08:50 am

  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

  • Meeting 52 : Tue, Mar 18, 11:00 am-11:50 am

  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

  • Meeting 53 : Thu, Mar 27, 01:00 pm-01:50 pm

  ShoT 03: <br> Syllabus : Lectures 32 - 37

  References
  Exercises
  Reading

  ShoT 03:
  Syllabus : Lectures 32 - 37
  

  References

  :

  None

  • Meeting 54 : Tue, Apr 08, 08:00 am-08:50 am

  Quiz - II <br> Syllabus : Lectures 22-40

  References
  Exercises
  Reading

  Quiz - II
  Syllabus : Lectures 22-40
  

  References

  :

  None

  • Meeting 55 : Mon, Apr 28, 11:00 am-11:50 am

  ShoT 04 <br> Lecture 42 - 49.

  References
  Exercises
  Reading

  ShoT 04
  Lecture 42 - 49.
  

  References

  :

  None

  • Meeting 56 : Tue, May 06, 09:00 am-12:00 pm

  Endsemester Exam

  References
  Exercises
  Reading

  Endsemester Exam
  

  References

  :

  None

• Theme 6 : Tutorial Meetings - 5 meetings

  • Meeting 57 : Thu, Jan 30, 02:00 pm-03:00 pm

  IDOT 01 (optional attendance)

  References
  Exercises
  Reading

  IDOT 01 (optional attendance)
  

  References

  :

  None

  • Meeting 58 : Thu, Feb 20, 10:00 am-10:50 am

  IDOT 02 (optional attendance)

  References
  Exercises
  Reading

  IDOT 02 (optional attendance)
  

  References

  :

  None

  • Meeting 59 : Thu, Mar 06, 10:00 am-10:50 am

  IDOT 03 (optional attendance)

  References
  Exercises
  Reading

  IDOT 03 (optional attendance)
  

  References

  :

  None

  • Meeting 60 : Thu, Apr 03, 10:00 am-10:50 am

  IDOT 04 (Optional Attendance)

  References
  Exercises
  Reading

  IDOT 04 (Optional Attendance)
  

  References

  :

  None

  • Meeting 61 : Thu, Apr 17, 02:00 pm-03:00 pm

  IDOT 05 (optional attendance)

  References
  Exercises
  Reading

  IDOT 05 (optional attendance)
  

  References

  :

  None