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07 - 7 Properties of regular languages Theorem 1 The set of...

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7: Properties of regular languages Theorem 1 The set of regular languages are closed under 1. Concatenation ( L 1 and L 2 regular, then so is L 1 L 2 ), 2. Union ( L 1 and L 2 regular, then so is L 1 L 2 ), 3. Kleene star ( L regular, then so is L ), 4. Complementation ( L regular, then so is L L ), and 5. Intersection ( L 1 and L 2 regular, then so is L 1 L 2 ). 1
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: 1.-3. We have seen two ways of proving these statements in earlier lecture notes. The Frst way is to show that there exists a regular expression that represents the resulting language, the second way is to show that there exists an (N)±A that accepts the resulting language. 4. Since L is regular, L is accepted by some D±A M . Let M ± be the same as M except that: A state is a Fnal state in M ± i² it is not a Fnal state in M . L is accepted by the D±A M ± . Hence, L is regular. 5. L 1 L 2 = L 1 L 2 . Since the set of all regular languages is closed under
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  • Spring '10
  • Prof.Tai
  • Formal language, Regular expression, Regular language, Nondeterministic finite state machine, decimal representation, Kleene star

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07 - 7 Properties of regular languages Theorem 1 The set of...

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