lec04 - Equivalence of DFA and Regular Expressions CSCI...

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1/19 Equivalence of DFA and Regular Expressions CSCI 3130 Formal Languages and Automata Theory Siu On CHAN Chinese University of Hong Kong Fall 2015
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2/19 Three ways of doing it [ = { Σ * | ends in 01 } Σ = { 0 , 1 } z 0 z 1 z 2 1 0 0 1 0 1 z 0 z 1 z 2 0,1 0 1 ( 0 + 1 ) * 01 DFA NFA regular expressions
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3/19 They are equally powerful DFA NFA regular expressions regular languages
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4/19 Roadmap regular expressions NFA NFA without ε DFA 3 3
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5/19 Examples: regular expression NFA ~ 1 = 0 z 0 z 1 0 ~ 2 = 01 z 0 z 1 z 2 0 1
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6/19 Examples: regular expression NFA ~ 3 = 0 + 01 NFA 3 z 0 z 1 z 2 z 2 z 3 z 4 z 5 z 6 ε 0 ε ε 0 1 ε ~ 4 = ( 0 + 01 ) * z 0 0 NFA 3 z 0 1 ε ε ε ε
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7/19 Regular expressions In general, how do we convert a regular expression to an NFA? A regular expression over Σ is an expression formed by the following rules I The symbols and ε are regular expressions I Every a in Σ is a regular expression I If ~ asd ¢ are regular expressions, so are ~ + ¢ , and ~ *
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8/19 General method regular expression S NFA z 0 ε z 0 a Σ z 0 z 1 a
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9/19 General method regular expression S
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