{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

This preview shows pages 1–3. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
: 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
This is the end of the preview. Sign up to access the rest of the document.
• Spring '10
• Prof.Tai
• Formal language, Regular expression, Regular language, Nondeterministic finite state machine, decimal representation, Kleene star

{[ snackBarMessage ]}

### Page1 / 5

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online