Note for FORMAL LANGUAGES AND AUTOMATA THEORY - FLAT By JNTU Heroes

Topics ( 5 )

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Formal Languages & Automata Theory Complete Notes

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Contents 1 Mathematical Preliminaries 3 2 Formal Languages 2.1 Strings . . . . . . . . . . . . 2.2 Languages . . . . . . . . . . 2.3 Properties . . . . . . . . . . 2.4 Finite Representation . . . . 2.4.1 Regular Expressions 3 Grammars 3.1 Context-Free Grammars 3.2 Derivation Trees . . . . . 3.2.1 Ambiguity . . . . 3.3 Regular Grammars . . . 3.4 Digraph Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Finite Automata 4.1 Deterministic Finite Automata . . . . . . . . . . . 4.2 Nondeterministic Finite Automata . . . . . . . . . 4.3 Equivalence of NFA and DFA . . . . . . . . . . . . 4.3.1 Heuristics to Convert NFA to DFA . . . . . 4.4 Minimization of DFA . . . . . . . . . . . . . . . . . 4.4.1 Myhill-Nerode Theorem . . . . . . . . . . . 4.4.2 Algorithmic Procedure for Minimization . . 4.5 Regular Languages . . . . . . . . . . . . . . . . . . 4.5.1 Equivalence of Finite Automata and Regular 4.5.2 Equivalence of Finite Automata and Regular 4.6 Variants of Finite Automata . . . . . . . . . . . . . 4.6.1 Two-way Finite Automaton . . . . . . . . . 4.6.2 Mealy Machines . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 . 5 . 6 . 10 . 13 . 13 . . . . . 18 19 26 31 32 36 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Languages Grammars . . . . . . . . . . . . . . . . . . 38 39 49 54 58 61 61 65 72 72 84 89 89 91

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5 Properties of Regular Languages 5.1 Closure Properties . . . . . . . 5.1.1 Set Theoretic Properties 5.1.2 Other Properties . . . . 5.2 Pumping Lemma . . . . . . . . 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 94 94 97 104

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Chapter 1 Mathematical Preliminaries 3