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Unformatted text preview: 1 Regular Expressions Definitions Equivalence to Finite Automata 2 REs: Introduction Regular expressions are an algebraic way to describe languages. They describe exactly the regular languages. If E is a regular expression, then L(E) is the language it defines. Well describe REs and their languages recursively. 3 REs: Definition Basis 1 : If a is any symbol, then a is a RE, and L( a ) = {a}. Note : {a} is the language containing one string, and that string is of length 1. Basis 2 : is a RE, and L( ) = { }. Basis 3 : is a RE, and L( ) = . 4 REs: Definition (2) Induction 1 : If E 1 and E 2 are regular expressions, then E 1 +E 2 is a regular expression, and L(E 1 +E 2 ) = L(E 1 ) L(E 2 ). Induction 2 : If E 1 and E 2 are regular expressions, then E 1 E 2 is a regular expression, and L(E 1 E 2 ) = L(E 1 )L(E 2 ). Concatenation : the set of strings wx such that w Is in L(E 1 ) and x is in L(E 2 ). 5 REs: Definition (3) Induction 3 : If E is a RE, then E* is a RE, and L(E*) = (L(E))*. Closure , or Kleene closure = set of strings w 1 w 2 w n , for some n > 0, where each w i is in L(E)....
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 Spring '08
 Motwani,R

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