Thoery of Automata CS402 mywbut.com Theory of Automata (CS402) Table of contents: Lecture N0. 1 .......................................................................................................................................................... 4 Summary............................................................................................................................................................ 4 What does automata mean? ............................................................................................................................... 4 Introduction to languages................................................................................................................................... 4 Alphabets ........................................................................................................................................................... 4 Strings................................................................................................................................................................ 4 Defining Languages........................................................................................................................................... 5 Lecture N0. 2 .......................................................................................................................................................... 9 Summary............................................................................................................................................................ 9 Kleene Star Closure ........................................................................................................................................... 9 Recursive definition of languages...................................................................................................................... 9 Lecture N0. 3 ........................................................................................................................................................ 11 Summary.......................................................................................................................................................... 11 Regular Expression.......................................................................................................................................... 11 Recursive definition of Regular Expression(RE)............................................................................................. 11 Method 3 (Regular Expressions) ..................................................................................................................... 11 Lecture N0. 4 ........................................................................................................................................................ 12 Equivalent Regular Expressions ...................................................................................................................... 12 Method 4 (Finite Automaton) .......................................................................................................................... 13 Lecture N0. 5 ........................................................................................................................................................ 15 Lecture N0. 6 ........................................................................................................................................................ 17 Equivalent FAs ................................................................................................................................................ 17 Lecture N0. 7 ........................................................................................................................................................ 20 FA corresponding to finite languages .............................................................................................................. 20 Method 5 (Transition Graph) ........................................................................................................................... 22 Lecture N0. 8 ........................................................................................................................................................ 23 Examples of TGs: accepting all strings, accepting none, starting with b, not ending in b, containing aa, containing aa or bb........................................................................................................................................... 23 Lecture N0. 9 ........................................................................................................................................................ 25 Generalized Transition Graphs ........................................................................................................................ 27 Lecture N0. 10 ...................................................................................................................................................... 28 Nondeterminism............................................................................................................................................... 29 Kleene’s Theorem............................................................................................................................................ 29 Lecture N0. 11 ...................................................................................................................................................... 30 Proof(Kleene’s Theorem Part II) ..................................................................................................................... 30 Lecture N0. 12 ...................................................................................................................................................... 34 Kleene’s Theorem Part III ............................................................................................................................... 35 Lecture N0. 13 ...................................................................................................................................................... 38 Lecture N0. 14 ...................................................................................................................................................... 41 Lecture N0. 15 ...................................................................................................................................................... 44 Nondeterministic Finite Automaton (NFA) .................................................................................................... 44 Converting an FA to an equivalent NFA ......................................................................................................... 45 Lecture N0. 16 ...................................................................................................................................................... 47 NFA with Null String ...................................................................................................................................... 47 Lecture N0. 17 ...................................................................................................................................................... 50 NFA and Kleene’s Theorem ............................................................................................................................ 50 Lecture N0. 18 ...................................................................................................................................................... 53 NFA corresponding to Concatenation of FAs.................................................................................................. 53 NFA corresponding to the Closure of an FA ................................................................................................... 55 Lecture N0. 19 ...................................................................................................................................................... 57 Memory required to recognize a language....................................................................................................... 57 Distinguishable strings and Indistinguishable strings ...................................................................................... 58 Lecture N0. 20 ...................................................................................................................................................... 60 Finite Automaton with output.......................................................................................................................... 60 Moore machine ................................................................................................................................................ 60 Lecture N0. 21 ...................................................................................................................................................... 62 Mealy machine................................................................................................................................................. 62 Lecture N0. 22 ...................................................................................................................................................... 65 2 mywbut.com Theory of Automata (CS402) Equivalent machines ........................................................................................................................................ 65 Lecture N0. 23 .....................................................................................................................................................