CS2200 - Languages, Machines and Computation

Meetings  

• Theme 1 : Finite Automata & Regular Languages - 23 meetings

  • Meeting 01 : Mon, Jan 11, 11:00 am-11:50 am

  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 bug

  • Meeting 02 : Wed, Jan 13, 09:00 am-09:50 am

  TA 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

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  None

  • Meeting 03 : Thu, Jan 14, 01:00 pm-01:50 pm

  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.

  • Meeting 04 : Mon, Jan 18, 11:00 am-11:50 am

  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

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  None

  • Meeting 05 : Tue, Jan 19, 10:00 pm-10:50 pm

  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?

  • Meeting 06 : Wed, Jan 20, 09:00 am-09:50 am

  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]

  • Meeting 07 : Wed, Jan 27, 09:00 am-09:50 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
  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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  None

  • Meeting 08 : Thu, Jan 28, 01:00 pm-01:50 pm

  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

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  None

  • Meeting 09 : Mon, Feb 01, 11:00 am-11:50 am

  Proof of the pumping Lemma. Applications.

  References
  Exercises
  Reading

  Proof of the pumping Lemma. Applications.
  

  References

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  None

  • Meeting 10 : Tue, Feb 02, 10:00 pm-10:50 pm

  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

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  None

  • Meeting 11 : Wed, Feb 03, 09:00 am-09:50 am

  Collapsing states in a finite automaton. Minimization.

  References
  Exercises
  Reading

  Collapsing states in a finite automaton. Minimization.
  

  References

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  None

  • Meeting 12 : Thu, Feb 04, 01:00 pm-01:50 pm

  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

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  None

  • Meeting 13 : Thu, Feb 04, 02:00 pm-02:50 pm

  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

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  None

  • Meeting 14 : Mon, Feb 08, 11:00 am-11:50 am

  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

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  None

  • Meeting 15 : Tue, Feb 09, 10:00 pm-10:50 pm

  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

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  None

  • Meeting 16 : Thu, Feb 11, 01:00 pm-01:50 pm

  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

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  None

  • Meeting 17 : Mon, Feb 15, 11:00 am-11:50 am

  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

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  None

  • Meeting 18 : Tue, Feb 16, 10:00 pm-10:50 pm

  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

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  None

  • Meeting 19 : Wed, Feb 17, 09:00 am-09:50 am

  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

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  None

  • Meeting 20 : Wed, Feb 24, 09:00 am-09:50 am

  TBA

  References
  Exercises
  Reading

  TBA
  

  References

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  None

  • Meeting 21 : Thu, Feb 25, 01:00 pm-01:50 pm

  Expressing languages using expressions.

  References
  Exercises
  Reading

  Expressing languages using expressions.
  

  References

  :

  None

  • Meeting 22 : Mon, Feb 29, 11:00 am-11:50 am

  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

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  None

  • Meeting 23 : Tue, Mar 01, 10:00 pm-10:50 pm

  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

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  None

• Theme 2 : Grammars & Context-free Languages - 13 meetings

  • Meeting 24 : Wed, Mar 02, 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

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  None

  • Meeting 25 : Thu, Mar 03, 01:00 pm-01:50 pm

  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

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  None

  • Meeting 26 : Mon, Mar 07, 11:00 am-11:50 am

  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

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  None

  • Meeting 27 : Tue, Mar 08, 10:00 pm-10:50 pm

  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

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  None

  • Meeting 28 : Thu, Mar 10, 01:00 pm-01:50 pm

  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

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  None

  • Meeting 29 : Mon, Mar 14, 11:00 am-11:50 am

  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

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  None

  • Meeting 30 : Tue, Mar 15, 10:00 pm-10:50 pm

  Derivations, Parse Trees and an intuition leading towards pumping lemma.

  References
  Exercises
  Reading

  Derivations, Parse Trees and an intuition leading towards pumping lemma.
  

  References

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  None

  • Meeting 31 : Wed, Mar 16, 09:00 am-09:50 am

  Pumping Lemma for CFLs. Proof and two applications.

  References
  Exercises
  Reading

  Pumping Lemma for CFLs. Proof and two applications.
  

  References

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  None

  • Meeting 32 : Mon, Mar 21, 11:00 am-11:50 am

  CYK Algorithm for CFLs

  References
  Exercises
  Reading

  CYK Algorithm for CFLs
  

  References

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  None

  • Meeting 33 : Tue, Mar 22, 10:00 pm-10:50 pm

  Towards a machine model for CFLs. Greibach Normal Form.

  References
  Exercises
  Reading

  Towards a machine model for CFLs. Greibach Normal Form.
  

  References

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  None

  • Meeting 34 : Wed, Mar 23, 09:00 am-09:50 am

  From a CFL in GNF to a PDA.

  References
  Exercises
  Reading

  From a CFL in GNF to a PDA.
  

  References

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  None

  • Meeting 35 : Mon, Mar 28, 11:00 am-11:50 am

  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

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  None

  • Meeting 36 : Wed, Mar 30, 09:00 am-09:50 am

  Finishing up the proof. Interesting Computational Problems about CFLs.

  References
  Exercises
  Reading

  Finishing up the proof. Interesting Computational Problems about CFLs.
  

  References

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  None

• Theme 3 : Turing Machines & Computability - 10 meetings

  • Meeting 37 : Thu, Mar 31, 01:00 pm-01:50 pm

  To Be Announced

  References
  Exercises
  Reading

  To Be Announced
  

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  None

  • Meeting 38 : Mon, Apr 04, 11:00 am-11:50 am

  To Be Announced

  References
  Exercises
  Reading

  To Be Announced
  

  References

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  None

  • Meeting 39 : Tue, Apr 05, 10:00 pm-10:50 pm

  To Be Announced

  References
  Exercises
  Reading

  To Be Announced
  

  References

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  None

  • Meeting 40 : Thu, Apr 07, 01:00 pm-01:50 pm

  To Be Announced

  References
  Exercises
  Reading

  To Be Announced
  

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  None

  • Meeting 41 : Mon, Apr 11, 11:00 am-11:50 am

  To Be Announced

  References
  Exercises
  Reading

  To Be Announced
  

  References

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  None

  • Meeting 42 : Tue, Apr 12, 10:00 pm-10:50 pm

  To Be Announced

  References
  Exercises
  Reading

  To Be Announced
  

  References

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  None

  • Meeting 43 : Wed, Apr 13, 09:00 am-09:50 am

  To Be Announced

  References
  Exercises
  Reading

  To Be Announced
  

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  None

  • Meeting 44 : Mon, Apr 18, 11:00 am-11:50 am

  To Be Announced

  References
  Exercises
  Reading

  To Be Announced
  

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  None

  • Meeting 45 : Tue, Apr 19, 10:00 pm-10:50 pm

  To Be Announced

  References
  Exercises
  Reading

  To Be Announced
  

  References

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  None

  • Meeting 46 : Mon, Apr 25, 11:00 am-11:50 am

  To Be Announced

  References
  Exercises
  Reading

  To Be Announced
  

  References

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  None

• Theme 4 : Evaluation & Tutorial Meetings - 12 meetings

  • Meeting 47 : Thu, Jan 21, 01:00 pm-01:50 pm

  DoT 01

  References
  Exercises
  Reading

  DoT 01
  

  References

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  None

  • Meeting 48 : Wed, Feb 10, 09:00 am-09:50 am

  ShoT 01

  References
  Exercises
  Reading

  ShoT 01
  

  References

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  None

  • Meeting 49 : Thu, Feb 18, 01:00 pm-01:50 pm

  DoT 02

  References
  Exercises
  Reading

  DoT 02
  

  References

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  None

  • Meeting 50 : Tue, Feb 23, 10:00 pm-10:50 pm

  Quiz - I

  References
  Exercises
  Reading

  Quiz - I
  

  References

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  None

  • Meeting 51 : Thu, Mar 03, 02:00 pm-02:50 pm

  DoT 03

  References
  Exercises
  Reading

  DoT 03
  

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  None

  • Meeting 52 : Wed, Mar 09, 09:00 am-09:50 am

  ShoT 02

  References
  Exercises
  Reading

  ShoT 02
  

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  None

  • Meeting 53 : Thu, Mar 17, 01:00 pm-01:50 pm

  DoT 03-a

  References
  Exercises
  Reading

  DoT 03-a
  

  References

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  None

  • Meeting 54 : Tue, Mar 29, 08:00 am-08:50 am

  Quiz - II

  References
  Exercises
  Reading

  Quiz - II
  

  References

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  None

  • Meeting 55 : Wed, Apr 06, 09:00 am-09:50 am

  ShoT 03

  References
  Exercises
  Reading

  ShoT 03
  

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  None

  • Meeting 56 : Thu, Apr 21, 01:00 pm-01:50 pm

  DoT 04

  References
  Exercises
  Reading

  DoT 04
  

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  None

  • Meeting 57 : Tue, Apr 26, 10:00 pm-10:50 pm

  ShoT 04

  References
  Exercises
  Reading

  ShoT 04
  

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  None

  • Meeting 58 : Tue, May 03, 09:00 am-12:00 pm

  Endsem

  References
  Exercises
  Reading

  Endsem
  

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  None