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      Dr. Madhu Mutyam
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IIT Madras
      Dr. V.Masilamani
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IIITD&M


Untitled Document

Grammars - Production systems - Chomskian Hierarchy - Right linear grammar and Finite state automata - Context free grammars - Normal forms - uvwxy theorem – Parikh mapping - Self embedding property - Subfamilies of CFL - Derivation trees and ambiguity.

Finite state Automata - Non deterministic and deterministic FSA, NFSA with ε- moves, Regular Expressions - Equivalence of regular expression and FSA .

Pumping lemma , closure properties and decidability. Myhill - Nerode theorem and minimization - Finite automata with output.

Pushdown automata - Acceptance by empty store and final state - Equivalence between pushdown automata and context-free grammars - Closure properties of CFL - Deterministic pushdown automata.

Turing Machines - Techniques for Turing machine construction - Generalized and restricted versions equivalent to the basic model - Godel numbering - Universal Turing Machine - Recursively enumerable sets and recursive sets - Computable functions - time space complexity measures - context sensitive languages and linear bound automata.

Decidability; Post's correspondence problem; Rice's theorem; decidability of membership, emptiness and equivalence problems of languages.

Time and tape complexity measures of Turing machines; Random access machines; the classes P and NP; NP-Completeness; satisfiability and Cook's theorem; Polynomial reduction and some NP-complete problems.

Advanced topics; Regulated rewriting L systems; Grammar systems.

New paradigms of computing; DNA computing; Membrane computing.



Module No.

Topics

No. of Hours

1

Grammars, Languages generated, Chomskian Hierarchy, CFG, Ambiguity, Reduced grammars, Normal forms

7

2

FSA,NFSA, NFSA with € moves, Regular expressions, Equivalence of regular expression and FSA, Equivalence of type 3 grammars and FSA, Pumping lemma , Closure and decidability results , Myhill- Nerode theorem, Minimization, FSA with output, Problems

11

3

Pushdown Automata, Acceptance by final state and empty store, Equivalence to CFG , Deterministic PDA

4

4

Problems and Solutions

3

5

Turing Machines - Construction, Techniques of TM construction , TM as acceptor and i/o device , Problems . Generalized and restricted versions.

5

6

Halting problems - Universal TM-recursive and recursively enumerable sets - Decidability - Rice’s Theorem , PCP

4

7

Time and Tape complexity of TM , P and NP, Cook’s theorem - NP-Complete Problems .

3

8

Advanced topics , Regulated rewritin , L systems Grammar system.

3

9

New Paradigms of computing , DNA computing , Membrane computing

2

Total

42

A basic knowledge in Mathematics. Some knowledge about sets, Relations and function is desirable.


  1. K.Krithivasan and R.Rama; Introduction to Formal Languages, Automata Theory and Computation; Pearson Education, 2009.

  2. J.E.Hopcroft, R.Motwani and J.D.Ullman , "Introduction to Automata Theory Languages and computation", Pearson Education Asia , 2001.


www.pearsoned.co.in/KamalaKrithivasan


  1. Peter Linz, "An Introduction to Formal Language and Automata", 4th Edition, Narosa Publishing house , 2006.

  2. M.Sipser; Introduction to the Theory of Computation; Singapore: Brooks/Cole, Thomson Learning, 1997.

  3. John.C.martin, "Introduction to the Languages and the Theory of Computation",Third edition, Tata McGrawHill, 2003.



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