1 / 8

DS020 오토마타형식언어

DS020 오토마타형식언어. Chapter 8. PROPERTIES OF CONTEXT-FREE LANGUAGES Exercises. 8.1 TWO PUMPING LEMMAS. 7. Show that the following languages on are not context-free. w = a (m-1)^3 b m. Solution. (m-1) 3 m. a … … a b … b. 1) |vxy| 2) |v x y|

dcale
Download Presentation

DS020 오토마타형식언어

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. DS020 오토마타형식언어 Chapter 8. PROPERTIES OF CONTEXT-FREE LANGUAGES Exercises

  2. 8.1 TWO PUMPING LEMMAS 7. Show that the following languages on are not context-free. w = a(m-1)^3bm Solution (m-1)3 m a … … a b … b 1) |vxy| 2) |v x y| 3) |vxy| i = 0 If |v| = 0  i = 2, else if |y| = 0  i = 0, otherwise (*) i = 2 i = 2  a는 (m-1)3 + k1개, b는 (m+k2)개 (m+k2-1)3≥ m3 = (m-1)3 + 3m2 -3m + 1 > (m-1)3 + k1 따라서 pumping된 문자열은 L에 속하지 않게 됨  Not CFL

  3. 8.1 TWO PUMPING LEMMAS w = ambmcm+1 Solution m m m+1 a … a b … b c … c • |vxy| • 2) |v x y| • 3) |vxy| • 4) |v x y| • 5) |vxy| i = 2 i = 2 i = 2 If |y| = 0  i = 2, otherwise i = 0 i = 0

  4. 8.1 TWO PUMPING LEMMAS w = ambm+1cm+1 Solution m m+1 m+1 a … a b … b c … c • |vxy| • 2) |v x y| • 3) |vxy| • 4) |v x y| • 5) |vxy| i = 2 If |y| = 0  i = 2, otherwise i = 0 i = 0 If |v| = 0  i = 2, otherwise i = 0 i = 2

  5. 8.1 TWO PUMPING LEMMAS 11. Show that the languageis context-free but not linear. Solution • 1) context free grammar • S  S1 S2 • S1  a S1 b | λ • S2  a S2 b | λ • 2) not linear w = ambm ambm m m m m a … a b … b a … ab … b |uv| |yz| i = 2

  6. 8.2 CLOSURE PROPERTIES AND DECISION ALGORITHMS FOR CONTEXT-FREE LANGUAGES 6. Which of the language families we have discussed are not closed under reversal?

  7. 8.2 CLOSURE PROPERTIES AND DECISION ALGORITHMS FOR CONTEXT-FREE LANGUAGES 10. Show that the family of linear language is not closed under intersection.

  8. 8.2 CLOSURE PROPERTIES AND DECISION ALGORITHMS FOR CONTEXT-FREE LANGUAGES 19. Is the family of deterministic context-free languages closed under homomorphism?

More Related