Pushdown Automata PDAs 1 Pushdown Automaton PDA Input
![Pushdown Automata PDAs 1 Pushdown Automata PDAs 1](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-1.jpg)
![Pushdown Automaton -- PDA Input String Stack States 2 Pushdown Automaton -- PDA Input String Stack States 2](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-2.jpg)
![Initial Stack Symbol Stack bottom special symbol 3 Initial Stack Symbol Stack bottom special symbol 3](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-3.jpg)
![The States Input symbol Pop symbol Push symbol 4 The States Input symbol Pop symbol Push symbol 4](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-4.jpg)
![input stack top 5 input stack top 5](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-5.jpg)
![input stack top 6 input stack top 6](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-6.jpg)
![input stack top 7 input stack top 7](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-7.jpg)
![input stack top 8 input stack top 8](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-8.jpg)
![Non-Determinism 9 Non-Determinism 9](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-9.jpg)
![NPDA: Non-Deterministic PDA Example: 10 NPDA: Non-Deterministic PDA Example: 10](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-10.jpg)
![Execution Example: Time 0 Input Stack current state 11 Execution Example: Time 0 Input Stack current state 11](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-11.jpg)
![Time 1 Input Stack 12 Time 1 Input Stack 12](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-12.jpg)
![Time 2 Input Stack 13 Time 2 Input Stack 13](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-13.jpg)
![Time 3 Input Stack 14 Time 3 Input Stack 14](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-14.jpg)
![Time 4 Input Stack 15 Time 4 Input Stack 15](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-15.jpg)
![Time 5 Input Stack 16 Time 5 Input Stack 16](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-16.jpg)
![Time 6 Input Stack 17 Time 6 Input Stack 17](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-17.jpg)
![Time 7 Input Stack 18 Time 7 Input Stack 18](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-18.jpg)
![Time 8 Input Stack accept 19 Time 8 Input Stack accept 19](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-19.jpg)
![A string is accepted if: • All the input is consumed • The last A string is accepted if: • All the input is consumed • The last](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-20.jpg)
![The input string is accepted by the NPDA: 21 The input string is accepted by the NPDA: 21](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-21.jpg)
![In general, is the language accepted by the NPDA: 22 In general, is the language accepted by the NPDA: 22](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-22.jpg)
![Another NPDA example NPDA 23 Another NPDA example NPDA 23](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-23.jpg)
![24 24](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-24.jpg)
![Execution Example: Time 0 Input Stack 25 Execution Example: Time 0 Input Stack 25](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-25.jpg)
![Time 1 Input Stack 26 Time 1 Input Stack 26](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-26.jpg)
![Time 2 Input Stack 27 Time 2 Input Stack 27](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-27.jpg)
![Time 3 Input Stack 28 Time 3 Input Stack 28](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-28.jpg)
![Time 4 Input Stack 29 Time 4 Input Stack 29](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-29.jpg)
![Time 5 Input Stack 30 Time 5 Input Stack 30](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-30.jpg)
![Time 6 Input Stack accept 31 Time 6 Input Stack accept 31](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-31.jpg)
![Pushing Strings Input symbol Pop symbol Push string 32 Pushing Strings Input symbol Pop symbol Push string 32](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-32.jpg)
![Example: input stack top pushed string 33 Example: input stack top pushed string 33](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-33.jpg)
![Another NPDA example NPDA 34 Another NPDA example NPDA 34](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-34.jpg)
![35 35](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-35.jpg)
![Execution: Time 0 Input Stack current state 36 Execution: Time 0 Input Stack current state 36](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-36.jpg)
![Time 1 Input Stack 37 Time 1 Input Stack 37](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-37.jpg)
![Time 3 Input Stack 38 Time 3 Input Stack 38](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-38.jpg)
![Time 4 Input Stack 39 Time 4 Input Stack 39](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-39.jpg)
![Time 5 Input Stack 40 Time 5 Input Stack 40](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-40.jpg)
![Time 6 Input Stack 41 Time 6 Input Stack 41](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-41.jpg)
![Time 7 Input Stack 42 Time 7 Input Stack 42](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-42.jpg)
![Time 8 Input Stack accept 43 Time 8 Input Stack accept 43](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-43.jpg)
![Formalities for NPDAs 44 Formalities for NPDAs 44](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-44.jpg)
![Transition function: 45 Transition function: 45](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-45.jpg)
![Transition function: 46 Transition function: 46](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-46.jpg)
![Formal Definition Non-Deterministic Pushdown Automaton NPDA Final states States Input alphabet Stack alphabet Transition Formal Definition Non-Deterministic Pushdown Automaton NPDA Final states States Input alphabet Stack alphabet Transition](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-47.jpg)
![Instantaneous Description Current state Remaining input Current stack contents 48 Instantaneous Description Current state Remaining input Current stack contents 48](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-48.jpg)
![Example: Instantaneous Description Time 4: Input Stack 49 Example: Instantaneous Description Time 4: Input Stack 49](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-49.jpg)
![Example: Instantaneous Description Time 5: Input Stack 50 Example: Instantaneous Description Time 5: Input Stack 50](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-50.jpg)
![We write: (Time 4) (Time 5) 51 We write: (Time 4) (Time 5) 51](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-51.jpg)
![A computation: 52 A computation: 52](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-52.jpg)
![For convenience we write: 53 For convenience we write: 53](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-53.jpg)
![Formal Definition Language of NPDA Start state : Final state 54 Formal Definition Language of NPDA Start state : Final state 54](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-54.jpg)
![Example: thus NPDA : 55 Example: thus NPDA : 55](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-55.jpg)
![thus NPDA : 56 thus NPDA : 56](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-56.jpg)
![Therefore: NPDA : 57 Therefore: NPDA : 57](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-57.jpg)
![Converting Context-Free Grammars to NPDAs 58 Converting Context-Free Grammars to NPDAs 58](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-58.jpg)
![An example grammar: What is the equivalent NPDA? 59 An example grammar: What is the equivalent NPDA? 59](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-59.jpg)
![Grammar: NPDA: 60 Grammar: NPDA: 60](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-60.jpg)
![The NPDA simulates leftmost derivations of the grammar L(grammar) = L(NPDA) 61 The NPDA simulates leftmost derivations of the grammar L(grammar) = L(NPDA) 61](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-61.jpg)
![Grammar: A leftmost derivation: 62 Grammar: A leftmost derivation: 62](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-62.jpg)
![NPDA execution: Time 0 Input Stack current state 63 NPDA execution: Time 0 Input Stack current state 63](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-63.jpg)
![Time 1 Input Stack 64 Time 1 Input Stack 64](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-64.jpg)
![Time 2 Input Stack 65 Time 2 Input Stack 65](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-65.jpg)
![Time 3 Input Stack 66 Time 3 Input Stack 66](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-66.jpg)
![Time 4 Input Stack 67 Time 4 Input Stack 67](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-67.jpg)
![Time 5 Input Stack 68 Time 5 Input Stack 68](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-68.jpg)
![Time 6 Input Stack 69 Time 6 Input Stack 69](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-69.jpg)
![Time 7 Input Stack 70 Time 7 Input Stack 70](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-70.jpg)
![Time 8 Input Stack 71 Time 8 Input Stack 71](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-71.jpg)
![Time 9 Input Stack 72 Time 9 Input Stack 72](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-72.jpg)
![Time 10 Input Stack accept 73 Time 10 Input Stack accept 73](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-73.jpg)
![In general: Given any grammar We can construct a NPDA With 74 In general: Given any grammar We can construct a NPDA With 74](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-74.jpg)
![Constructing NPDA from grammar : For any production For any terminal 75 Constructing NPDA from grammar : For any production For any terminal 75](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-75.jpg)
![Grammar generates string if and only if NPDA accepts 76 Grammar generates string if and only if NPDA accepts 76](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-76.jpg)
![Therefore: For any context-free language there is an NPDA that accepts the same language Therefore: For any context-free language there is an NPDA that accepts the same language](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-77.jpg)
- Slides: 77
![Pushdown Automata PDAs 1 Pushdown Automata PDAs 1](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-1.jpg)
Pushdown Automata PDAs 1
![Pushdown Automaton PDA Input String Stack States 2 Pushdown Automaton -- PDA Input String Stack States 2](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-2.jpg)
Pushdown Automaton -- PDA Input String Stack States 2
![Initial Stack Symbol Stack bottom special symbol 3 Initial Stack Symbol Stack bottom special symbol 3](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-3.jpg)
Initial Stack Symbol Stack bottom special symbol 3
![The States Input symbol Pop symbol Push symbol 4 The States Input symbol Pop symbol Push symbol 4](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-4.jpg)
The States Input symbol Pop symbol Push symbol 4
![input stack top 5 input stack top 5](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-5.jpg)
input stack top 5
![input stack top 6 input stack top 6](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-6.jpg)
input stack top 6
![input stack top 7 input stack top 7](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-7.jpg)
input stack top 7
![input stack top 8 input stack top 8](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-8.jpg)
input stack top 8
![NonDeterminism 9 Non-Determinism 9](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-9.jpg)
Non-Determinism 9
![NPDA NonDeterministic PDA Example 10 NPDA: Non-Deterministic PDA Example: 10](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-10.jpg)
NPDA: Non-Deterministic PDA Example: 10
![Execution Example Time 0 Input Stack current state 11 Execution Example: Time 0 Input Stack current state 11](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-11.jpg)
Execution Example: Time 0 Input Stack current state 11
![Time 1 Input Stack 12 Time 1 Input Stack 12](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-12.jpg)
Time 1 Input Stack 12
![Time 2 Input Stack 13 Time 2 Input Stack 13](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-13.jpg)
Time 2 Input Stack 13
![Time 3 Input Stack 14 Time 3 Input Stack 14](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-14.jpg)
Time 3 Input Stack 14
![Time 4 Input Stack 15 Time 4 Input Stack 15](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-15.jpg)
Time 4 Input Stack 15
![Time 5 Input Stack 16 Time 5 Input Stack 16](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-16.jpg)
Time 5 Input Stack 16
![Time 6 Input Stack 17 Time 6 Input Stack 17](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-17.jpg)
Time 6 Input Stack 17
![Time 7 Input Stack 18 Time 7 Input Stack 18](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-18.jpg)
Time 7 Input Stack 18
![Time 8 Input Stack accept 19 Time 8 Input Stack accept 19](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-19.jpg)
Time 8 Input Stack accept 19
![A string is accepted if All the input is consumed The last A string is accepted if: • All the input is consumed • The last](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-20.jpg)
A string is accepted if: • All the input is consumed • The last state is a final state We do not care about the stack contents 20
![The input string is accepted by the NPDA 21 The input string is accepted by the NPDA: 21](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-21.jpg)
The input string is accepted by the NPDA: 21
![In general is the language accepted by the NPDA 22 In general, is the language accepted by the NPDA: 22](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-22.jpg)
In general, is the language accepted by the NPDA: 22
![Another NPDA example NPDA 23 Another NPDA example NPDA 23](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-23.jpg)
Another NPDA example NPDA 23
![24 24](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-24.jpg)
24
![Execution Example Time 0 Input Stack 25 Execution Example: Time 0 Input Stack 25](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-25.jpg)
Execution Example: Time 0 Input Stack 25
![Time 1 Input Stack 26 Time 1 Input Stack 26](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-26.jpg)
Time 1 Input Stack 26
![Time 2 Input Stack 27 Time 2 Input Stack 27](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-27.jpg)
Time 2 Input Stack 27
![Time 3 Input Stack 28 Time 3 Input Stack 28](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-28.jpg)
Time 3 Input Stack 28
![Time 4 Input Stack 29 Time 4 Input Stack 29](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-29.jpg)
Time 4 Input Stack 29
![Time 5 Input Stack 30 Time 5 Input Stack 30](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-30.jpg)
Time 5 Input Stack 30
![Time 6 Input Stack accept 31 Time 6 Input Stack accept 31](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-31.jpg)
Time 6 Input Stack accept 31
![Pushing Strings Input symbol Pop symbol Push string 32 Pushing Strings Input symbol Pop symbol Push string 32](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-32.jpg)
Pushing Strings Input symbol Pop symbol Push string 32
![Example input stack top pushed string 33 Example: input stack top pushed string 33](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-33.jpg)
Example: input stack top pushed string 33
![Another NPDA example NPDA 34 Another NPDA example NPDA 34](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-34.jpg)
Another NPDA example NPDA 34
![35 35](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-35.jpg)
35
![Execution Time 0 Input Stack current state 36 Execution: Time 0 Input Stack current state 36](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-36.jpg)
Execution: Time 0 Input Stack current state 36
![Time 1 Input Stack 37 Time 1 Input Stack 37](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-37.jpg)
Time 1 Input Stack 37
![Time 3 Input Stack 38 Time 3 Input Stack 38](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-38.jpg)
Time 3 Input Stack 38
![Time 4 Input Stack 39 Time 4 Input Stack 39](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-39.jpg)
Time 4 Input Stack 39
![Time 5 Input Stack 40 Time 5 Input Stack 40](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-40.jpg)
Time 5 Input Stack 40
![Time 6 Input Stack 41 Time 6 Input Stack 41](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-41.jpg)
Time 6 Input Stack 41
![Time 7 Input Stack 42 Time 7 Input Stack 42](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-42.jpg)
Time 7 Input Stack 42
![Time 8 Input Stack accept 43 Time 8 Input Stack accept 43](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-43.jpg)
Time 8 Input Stack accept 43
![Formalities for NPDAs 44 Formalities for NPDAs 44](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-44.jpg)
Formalities for NPDAs 44
![Transition function 45 Transition function: 45](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-45.jpg)
Transition function: 45
![Transition function 46 Transition function: 46](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-46.jpg)
Transition function: 46
![Formal Definition NonDeterministic Pushdown Automaton NPDA Final states States Input alphabet Stack alphabet Transition Formal Definition Non-Deterministic Pushdown Automaton NPDA Final states States Input alphabet Stack alphabet Transition](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-47.jpg)
Formal Definition Non-Deterministic Pushdown Automaton NPDA Final states States Input alphabet Stack alphabet Transition function Stack start symbol 47
![Instantaneous Description Current state Remaining input Current stack contents 48 Instantaneous Description Current state Remaining input Current stack contents 48](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-48.jpg)
Instantaneous Description Current state Remaining input Current stack contents 48
![Example Instantaneous Description Time 4 Input Stack 49 Example: Instantaneous Description Time 4: Input Stack 49](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-49.jpg)
Example: Instantaneous Description Time 4: Input Stack 49
![Example Instantaneous Description Time 5 Input Stack 50 Example: Instantaneous Description Time 5: Input Stack 50](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-50.jpg)
Example: Instantaneous Description Time 5: Input Stack 50
![We write Time 4 Time 5 51 We write: (Time 4) (Time 5) 51](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-51.jpg)
We write: (Time 4) (Time 5) 51
![A computation 52 A computation: 52](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-52.jpg)
A computation: 52
![For convenience we write 53 For convenience we write: 53](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-53.jpg)
For convenience we write: 53
![Formal Definition Language of NPDA Start state Final state 54 Formal Definition Language of NPDA Start state : Final state 54](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-54.jpg)
Formal Definition Language of NPDA Start state : Final state 54
![Example thus NPDA 55 Example: thus NPDA : 55](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-55.jpg)
Example: thus NPDA : 55
![thus NPDA 56 thus NPDA : 56](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-56.jpg)
thus NPDA : 56
![Therefore NPDA 57 Therefore: NPDA : 57](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-57.jpg)
Therefore: NPDA : 57
![Converting ContextFree Grammars to NPDAs 58 Converting Context-Free Grammars to NPDAs 58](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-58.jpg)
Converting Context-Free Grammars to NPDAs 58
![An example grammar What is the equivalent NPDA 59 An example grammar: What is the equivalent NPDA? 59](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-59.jpg)
An example grammar: What is the equivalent NPDA? 59
![Grammar NPDA 60 Grammar: NPDA: 60](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-60.jpg)
Grammar: NPDA: 60
![The NPDA simulates leftmost derivations of the grammar Lgrammar LNPDA 61 The NPDA simulates leftmost derivations of the grammar L(grammar) = L(NPDA) 61](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-61.jpg)
The NPDA simulates leftmost derivations of the grammar L(grammar) = L(NPDA) 61
![Grammar A leftmost derivation 62 Grammar: A leftmost derivation: 62](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-62.jpg)
Grammar: A leftmost derivation: 62
![NPDA execution Time 0 Input Stack current state 63 NPDA execution: Time 0 Input Stack current state 63](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-63.jpg)
NPDA execution: Time 0 Input Stack current state 63
![Time 1 Input Stack 64 Time 1 Input Stack 64](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-64.jpg)
Time 1 Input Stack 64
![Time 2 Input Stack 65 Time 2 Input Stack 65](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-65.jpg)
Time 2 Input Stack 65
![Time 3 Input Stack 66 Time 3 Input Stack 66](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-66.jpg)
Time 3 Input Stack 66
![Time 4 Input Stack 67 Time 4 Input Stack 67](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-67.jpg)
Time 4 Input Stack 67
![Time 5 Input Stack 68 Time 5 Input Stack 68](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-68.jpg)
Time 5 Input Stack 68
![Time 6 Input Stack 69 Time 6 Input Stack 69](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-69.jpg)
Time 6 Input Stack 69
![Time 7 Input Stack 70 Time 7 Input Stack 70](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-70.jpg)
Time 7 Input Stack 70
![Time 8 Input Stack 71 Time 8 Input Stack 71](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-71.jpg)
Time 8 Input Stack 71
![Time 9 Input Stack 72 Time 9 Input Stack 72](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-72.jpg)
Time 9 Input Stack 72
![Time 10 Input Stack accept 73 Time 10 Input Stack accept 73](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-73.jpg)
Time 10 Input Stack accept 73
![In general Given any grammar We can construct a NPDA With 74 In general: Given any grammar We can construct a NPDA With 74](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-74.jpg)
In general: Given any grammar We can construct a NPDA With 74
![Constructing NPDA from grammar For any production For any terminal 75 Constructing NPDA from grammar : For any production For any terminal 75](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-75.jpg)
Constructing NPDA from grammar : For any production For any terminal 75
![Grammar generates string if and only if NPDA accepts 76 Grammar generates string if and only if NPDA accepts 76](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-76.jpg)
Grammar generates string if and only if NPDA accepts 76
![Therefore For any contextfree language there is an NPDA that accepts the same language Therefore: For any context-free language there is an NPDA that accepts the same language](https://slidetodoc.com/presentation_image_h/0f983dbaaed9164c2f8e7339a29e3d3c/image-77.jpg)
Therefore: For any context-free language there is an NPDA that accepts the same language 77
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