Pushdown Automata PDAs 1 Pushdown Automaton PDA Input
- Slides: 90
Pushdown Automata PDAs 1
Pushdown Automaton -- PDA Input String Stack States 2
Initial Stack Symbol Stack stack head top bottom special symbol Appears at time 0 3
The States Input symbol Pop symbol Push symbol 4
input stack top Replace 5
input stack top Push 6
input stack top Pop 7
input stack top No Change 8
Empty Stack input stack top Pop empty The automaton HALTS No possible transition after 9
A Possible Transition input stack top Pop 10
Non-Determinism PDAs are non-deterministic Allowed non-deterministic transitions 11
Example PDA 12
Basic Idea: 1. Push the a’s 2. on the stack 2. Match the b’s on input with a’s on stack 3. Match found 13
Execution Example: Time 0 Input Stack current state 14
Time 1 Input Stack 15
Time 2 Input Stack 16
Time 3 Input Stack 17
Time 4 Input Stack 18
Time 5 Input Stack 19
Time 6 Input Stack 20
Time 7 Input Stack 21
Time 8 Input Stack accept 22
A string is accepted if there is a computation such that: All the input is consumed AND The last state is an accepting state At the end of the computation, we do not care about the stack contents (the stack can be empty at the last state) 23
The input string is accepted by the PDA: 24
In general, is the language accepted by the PDA: 25
Rejection Example: Time 0 Input Stack current state 26
Rejection Example: Time 1 Input Stack current state 27
Rejection Example: Time 2 Input Stack current state 28
Rejection Example: Time 3 Input Stack current state 29
Rejection Example: Time 4 Input Stack current state 30
Rejection Example: Time 4 Input reject Stack current state 31
The input string is rejected by the PDA: 32
A string is rejected if there is no computation such that: All the input is consumed AND The last state is an accept state At the end of the computation, we do not care about the stack contents 33
Another PDA example PDA 34
Basic Idea: 1. Push v 2. Guess 2. on stack middle of input 3. Match on input with v on stack 4. Match found 35
Execution Example: Time 0 Input Stack 36
Time 1 Input Stack 37
Time 2 Input Stack 38
Time 3 Input Guess the middle of string Stack 39
Time 4 Input Stack 40
Time 5 Input Stack 41
Time 6 Input Stack accept 42
Rejection Example: Time 0 Input Stack 43
Time 1 Input Stack 44
Time 2 Input Stack 45
Time 3 Input Guess the middle of string Stack 46
Time 4 Input Stack 47
Input Time 5 There is no possible transition. Input is not consumed Stack 48
Another computation on same string: Input Time 0 Stack 49
Time 1 Input Stack 50
Time 2 Input Stack 51
Time 3 Input Stack 52
Time 4 Input Stack 53
Time 5 Input No final state is reached Stack 54
There is no computation that accepts string 55
Another PDA example PDA 56
Execution Example: Time 0 Input Stack 57
Time 1 Input Stack 58
Time 2 Input Stack 59
Time 3 Input Stack accept 60
Rejection example: Time 0 Input Stack 61
Time 1 Input Stack 62
Time 2 Input Stack 63
Time 3 Input Stack 64
Time 4 Input Stack Halt and Reject 65
Pushing Strings Input symbol Pop symbol Push string 66
Example: input stack top pushed string Push 67
Another PDA example PDA 68
Execution Example: Time 0 Input Stack current state 69
Time 1 Input Stack 70
Time 3 Input Stack 71
Time 4 Input Stack 72
Time 5 Input Stack 73
Time 6 Input Stack 74
Time 7 Input Stack 75
Time 8 Input Stack accept 76
Formalities for PDAs 77
Transition function: 78
Transition function: 79
Formal Definition Pushdown Automaton (PDA) States Input alphabet Transition Initial Stack function state alphabet Final states Stack start symbol 80
Instantaneous Description Current state Remaining input Current stack contents 81
Example: Instantaneous Description Time 4: Input Stack 82
Example: Instantaneous Description Time 5: Input Stack 83
We write: Time 4 Time 5 84
A computation: 85
For convenience we write: 86
Formal Definition Language of PDA Initial state : Final state 87
Example: PDA : 88
PDA : 89
Therefore: PDA : 90
- Makalah push down automata
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