1 / 24

DPDA Deterministic PDA

DPDA Deterministic PDA. Deterministic PDA: DPDA. Allowed transitions:. (deterministic choices). Allowed transitions:. (deterministic choices). Not allowed:. (non deterministic choices). DPDA example. Definition:. A language is deterministic context-free

kaden-lara
Télécharger la présentation

DPDA Deterministic PDA

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. DPDADeterministic PDA Prof. Busch - LSU

  2. Deterministic PDA: DPDA Allowed transitions: (deterministic choices) Prof. Busch - LSU

  3. Allowed transitions: (deterministic choices) Prof. Busch - LSU

  4. Not allowed: (non deterministic choices) Prof. Busch - LSU

  5. DPDA example Prof. Busch - LSU

  6. Definition: A language is deterministic context-free if there exists some DPDA that accepts it Example: The language is deterministic context-free Prof. Busch - LSU

  7. Example of Non-DPDA (PDA) Prof. Busch - LSU

  8. Not allowed in DPDAs Prof. Busch - LSU

  9. PDAs Have More Power thanDPDAs Prof. Busch - LSU

  10. It holds that: Deterministic Context-Free Languages (DPDA) Context-Free Languages PDAs Since every DPDA is also a PDA Prof. Busch - LSU

  11. We will show that there exists a context-free language which is not accepted by any DPDA We will actually show: Deterministic Context-Free Languages (DPDA) Context-Free Languages (PDA) Prof. Busch - LSU

  12. The language is: We will show: • is context-free • is not deterministic context-free Prof. Busch - LSU

  13. Context-free grammar for : Language is context-free Prof. Busch - LSU

  14. Theorem: The language is not deterministic context-free (there is no DPDA that accepts ) Prof. Busch - LSU

  15. Proof: Assume for contradiction that is deterministic context free Therefore: there is a DPDA that accepts Prof. Busch - LSU

  16. DPDA with accepts accepts Prof. Busch - LSU

  17. DPDA with Such a path exists due to determinism Prof. Busch - LSU

  18. Context-free languages Regular languages Fact 1: The language is not context-free (we will prove this at a later class using pumping lemma for context-free languages) Prof. Busch - LSU

  19. Fact 2: The language is not context-free (we can prove this using pumping lemma for context-free languages) Prof. Busch - LSU

  20. We will construct a PDA that accepts: which is a contradiction! Prof. Busch - LSU

  21. DPDA Replace with Modify DPDA Prof. Busch - LSU

  22. A PDA that accepts Connect the final states of with the final states of Prof. Busch - LSU

  23. Since is accepted by a PDA it is context-free Contradiction! (since is not context-free) Prof. Busch - LSU

  24. Therefore: Is not deterministic context free There is no DPDA that accepts it End of Proof Prof. Busch - LSU

More Related