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Mathematics  Formal Languages and Automata Theory
Title: Formal Languages and Automata Theory
Department: Mathematics
Author: Dr. K.V. Krishna Dr. Diganta Goswami
University: IIT Guwahati
Type: WebLink
Abstract: Unit 1: (D. Goswami)
Introduction to the course. Texts and References are given.
Unit 2: (D. Goswami)
Alphabet, Strings, Languages, Finite Representation of languages, Regular Expressions.
Unit 3: (K. V. Krishna)
Context-free Grammars (CFGs) -Formal definition, sentential forms, leftmost and rightmost derivations,, the language of a CFG. Derivation tree or Parse tree -Definition, Relationship between parse trees and derivations. Parsing and ambiguity, Ambiguity in grammars and Languages. Regular grammars.
Unit 4: (D. Goswami)
Finite automata (FA) -its behavior; DFA -Formal definition, simplified notations (state transition diagram, transition table), Language of a DFA. NFA -Formal definition, Language of an NFA, Removing, epsilon-transitions. Equivalence of DFAs and NFAs.
Unit 5: (K. V. Krishna)
Myhill-Nerode Theorem and minimization of finite automata
Unit 6: (D. Goswami)
Establishing the equivalence between regular languages, regular grammars and finite automata.
Unit 7: (K. V. Krishna)
2DFA, Moore and Mealy automata.
Unit 8: (K. V. Krishna)
Some closure properties of Regular languages -Closure under Boolean operations, reversal, homomorphism, inverse homomorphism, etc. Pumping lemma, proving languages to be non regular.
Unit 9: (D. Goswami)
Simplification of CFGs -Removing useless symbols, epsilon- Productions, and unit productions, Normal forms -CNF and GNF
Unit 10: (K. V. Krishna)
Some closure properties of CFLs -Closure under union, concatenation, Kleene closure, substitution, homomorphism, reversal, intersection with regular set, etc. Pumping lemma.
Unit 11: (K. V. Krishna)
Pushdown automata and showing the equivalence between PDA and CFG.
Unit 12: (K. V. Krishna)
Turing Machines TM -Formal definition and behavior, Transition diagrams, Language of a TM, TM as accepters and deciders. TM as a computer of integer functions. Variants of Turing machines.
Unit 13: (K. V. Krishna)
Grammars and grammatically computable functions.
Unit 14: (D. Goswami)
Recursive languages, Some properties of recursive and recursively enumerable languages, Codes for TMs. A language that is not recursively enumerable (the diagonalization language). The universal language, Undecidability of the universal language, The Halting problem, Undecidable problems about TMs.
Unit 15: (K. V. Krishna)
Time bounded TMs, The classes P, NP and NP-complete, Cook s Theorem, Some NP-complete problems.
Unit 16: (D. Goswami)
Context-sensitive languages, linear bounded automata and Chomsky Hierarchy.
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