automata-3 - Automata Chapter 3 Regular Languages and...

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Unformatted text preview: Automata Chapter 3 Regular Languages and Regular Grammars 3.1 Regular Expressions Definition 3.1 Let be a given alphabet. Then 1. , , and a are all regular expressions. These are called primitive regular expressions. 1. If r 1 and r 2 are regular expressions, so are r 1 + r 2 , r 1 r 2 , r 1 *, and (r 1 ). 2. A string is a regular expression iff it can be derived from the primitive regular expressions by a finite number of applications of the rules in (2). 3.1 Regular Expressions Definition 3.2 The Language L( r ) denoted by any regular expression r is defined: 1. is a r.e. denoting the empty set. 2. is a r.e. denoting { }. 1. For every a , a is a r.e. denoting {a}. If r 1 and r 2 are regular expressions, then 4. L( r 1 + r 2 ) = L( r 1 ) L( r 2 ), 5. L( r 1 r 2 ) = L( r 1 )L( r 2 ), 6. L(( r 1 )) = L( r 1 ), 7. L( r 1 *) = (L( r 1 ))*. 3.1 Regular Expressions Ex. 3.1 (a+b c)* (c + ) Ex. 3.2 L(a * (a+b)) = L(a*) L(a+b) = (L(a))*(L(a) L(b)) = { ,a,aa,aaa, }{a,b} = {a,aa,aaa, . ,b, ab, aab, } 3.1 Regular Expressions Ex. 3.3 r = (a+b)* (a + bb) Ex. 3.4 r = (aa) * (bb)*b 3.1 Regular Expressions3....
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This note was uploaded on 11/03/2009 for the course CS automata taught by Professor Prof.jung during the Fall '09 term at 홍익대학교.

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automata-3 - Automata Chapter 3 Regular Languages and...

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