Formal Languages and Automata Theory

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Introduction – Alphabet, Strings, Languages, Finite Representation of languages, Regular Expressions – 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 – 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 – Myhill-Nerode Theorem and minimization of finite automata – Establishing the equivalence between regular languages, regular grammars and finite automata 2DFA, Moore and Mealy automata – Some closure properties of Regular languages -Closure under Boolean operations, reversal, homomorphism, inverse homomorphism, etc. Pumping lemma, proving languages to be non regular. – Simplification of CFGs

Removing useless symbols, epsilon- Productions, and unit productions, Normal forms -CNF and GNF – Some closure properties of CFLs -Closure under union, concatenation, Kleene closure, substitution,homomorphism, reversal, intersection with regular set, etc. Pumping lemma – Pushdown automata and showing the equivalence between PDA and CFG – 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 – Grammars and grammatically computable functions – 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 – Time bounded TMs, The classes P, NP and NP-complete, Cook’s Theorem, Some NP-complete problems – Context-sensitive languages, linear bounded automata and Chomsky Hierarchy.

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