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1 Some Properties of Regular Languages. 2 Properties Concatenation:Star: Union: Are regular Languages For regular languages and.

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Presentation on theme: "1 Some Properties of Regular Languages. 2 Properties Concatenation:Star: Union: Are regular Languages For regular languages and."— Presentation transcript:

1 1 Some Properties of Regular Languages

2 2 Properties Concatenation:Star: Union: Are regular Languages For regular languages and

3 3 We Say: Regular languages are closed under Concatenation:Star: Union:

4 4 Example

5 5 Union NFA for

6 6 Example NFA for

7 7 Concatenation NFA for

8 8 Example NFA for

9 9 Star Operation NFA for

10 10 Example NFA for

11 11 Regular Expressions

12 12 Regular Expressions Regular expressions describe regular languages Example: describes the language

13 13 Recursive Definition Are regular expressions Primitive regular expressions: Given regular expressions and

14 14 Examples A regular expression: Not a regular expression:

15 15 Languages of Regular Expressions : language of regular expression Example

16 16 Definition For primitive regular expressions:

17 17 Definition (continued) For regular expressions and

18 18 Example Regular expression:

19 19 Example Regular expression

20 20 Example Regular expression

21 21 Example Regular expression = { all strings with at least two consecutive 0 }

22 22 Example Regular expression = { all strings without two consecutive 0 }

23 23 Equivalent Regular Expressions Definition: Regular expressions and are equivalent if

24 24 Example = { all strings without two consecutive 0 } and are equivalent regular expr.

25 25 Theorem Languages Generated by Regular Expressions Regular Languages


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