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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

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DPDA Deterministic PDA

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  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

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