1 / 38

Regular Expressions

Regular Expressions. Regular Expressions. Regular expressions describe regular languages Example: describes the language. Given regular expressions and. Are regular expressions. Recursive Definition. Primitive regular expressions:. Not a regular expression:.

marny-mccoy
Download Presentation

Regular Expressions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Regular Expressions Prof. Busch - LSU

  2. Regular Expressions Regular expressions describe regular languages Example: describes the language Prof. Busch - LSU

  3. Given regular expressions and Are regular expressions Recursive Definition Primitive regular expressions: Prof. Busch - LSU

  4. Not a regular expression: Examples A regular expression: Prof. Busch - LSU

  5. Languages of Regular Expressions : language of regular expression Example Prof. Busch - LSU

  6. Definition For primitive regular expressions: Prof. Busch - LSU

  7. Definition (continued) For regular expressions and Prof. Busch - LSU

  8. Example Regular expression: Prof. Busch - LSU

  9. Example Regular expression Prof. Busch - LSU

  10. Example Regular expression Prof. Busch - LSU

  11. = { all strings containing substring 00 } Example Regular expression Prof. Busch - LSU

  12. = { all strings without substring 00 } Example Regular expression Prof. Busch - LSU

  13. Equivalent Regular Expressions Definition: Regular expressions and are equivalent if Prof. Busch - LSU

  14. and are equivalent regular expressions Example = { all strings without substring 00 } Prof. Busch - LSU

  15. Regular ExpressionsandRegular Languages Prof. Busch - LSU

  16. Theorem Languages Generated by Regular Expressions Regular Languages Prof. Busch - LSU

  17. Proof: Languages Generated by Regular Expressions Regular Languages Languages Generated by Regular Expressions Regular Languages Prof. Busch - LSU

  18. For any regular expression the language is regular Proof by induction on the size of Proof - Part 1 Languages Generated by Regular Expressions Regular Languages Prof. Busch - LSU

  19. regular languages Induction Basis Primitive Regular Expressions: Corresponding NFAs Prof. Busch - LSU

  20. Inductive Hypothesis Suppose that for regular expressions and , and are regular languages Prof. Busch - LSU

  21. Inductive Step We will prove: Are regular Languages Prof. Busch - LSU

  22. By definition of regular expressions: Prof. Busch - LSU

  23. We also know: Regular languages are closed under: Union Concatenation Star By inductive hypothesis we know: and are regular languages Prof. Busch - LSU

  24. Therefore: Are regular languages is trivially a regular language (by induction hypothesis) End of Proof-Part 1 Prof. Busch - LSU

  25. Using the regular closure of these operations, we can construct recursively the NFA that accepts Example: Prof. Busch - LSU

  26. Proof - Part 2 Languages Generated by Regular Expressions Regular Languages For any regular language there is a regular expression with We will convert an NFA that accepts to a regular expression Prof. Busch - LSU

  27. Since is regular, there is a NFA that accepts it Take it with a single accept state Prof. Busch - LSU

  28. From construct the equivalent Generalized Transition Graph in which transition labels are regular expressions Example: Corresponding Generalized transition graph Prof. Busch - LSU

  29. Another Example: Transition labels are regular expressions Prof. Busch - LSU

  30. Reducing the states: Transition labels are regular expressions Prof. Busch - LSU

  31. Resulting Regular Expression: Prof. Busch - LSU

  32. In General Removing a state: Prof. Busch - LSU

  33. By repeating the process until two states are left, the resulting graph is Initial graph Resulting graph The resulting regular expression: End of Proof-Part 2 Prof. Busch - LSU

  34. Standard Representations of Regular Languages Regular Languages DFAs Regular Expressions NFAs Prof. Busch - LSU

  35. When we say: We are given a Regular Language We mean: Language is in a standard representation (DFA, NFA, or Regular Expression) Prof. Busch - LSU

  36. Ekuivalensi NFA-ε Dengan ER (Ekspresi Regular) NFA- ε = NFA-λ (Automata Hingga Non-deterministik = NFA) atau λ atau r1 ˅ r2 atau r1 + r2 Prof. Busch - LSU

  37. Tentukan NFA untuk ekspresi regular r = 0(1|23)* Prof. Busch - LSU

  38. Prof. Busch - LSU

More Related