Theory of Computation Lecture 27 28 PDA A
- Slides: 46
Theory of Computation Lecture #27 -28
PDA �A pushdown automata (PDA) is basically an Є-NFA with a stack. �On a transition, the PDA: 1. Consumes an input symbol. 2. Goes to a new state (or stays in the old). 3. Replaces the top of the stack by any string (does nothing, pops the stack, or pushes a string onto the stack)
PDA �PDAs are like NFAs but have an extra component called a stack �The stack provides additional memory beyond the finite amount available in the control �The stack allows PDA to recognize some non-regular languages
PDA
PDA and CFG �PDA are equivalent in specification power with CFG �This is useful because it gives us two options for proving that a language is context-free: � 1. construct a CFG that generates the language or � 2. construct a PDA that recognizes the language
A PDA is described by
Pushdown Automaton -- PDA Input String Stack States 7
Initial Stack Symbol Stack stack head top bottom special symbol Appears at time 0 8
The States Input symbol Pop symbol Push symbol 9
Push Down Automata �An NFA with a stack �Can be used to represent Context free languages
Example
PDA �A PDA is a collection of
Input Tape
States
States
State Representation
State Representation
Stack
Example FA that accepts all words ending in the letter a
Example
Example FA that contains at least a double aa
Example PDA that contains at least a double aa
Stack Operations
n n ab Test - aaabbb
Example
Equivalent Machine is Try the strings: 1). aaabbbb 2). aaaabbb
Example of all states
Definition
Example CFG is
Example Cont…
Palindrome �Let us introduce the PALINDROMEX, language of all words of the form s X reverse(s) where s is any string in (a + b)* The words in this language are { X, a. Xa, b. Xb, aa. Xaa, ab. Xba, ba. Xab, bb. Xbb, aaa. Xaaa, aab. Xbaa. . . }
Palindrome Machine Start can be like this
Palindrome Machine
Palindrome Machine (Odd Palindrome) For odd palindrome (Guess middle alphabet). The problem here is that the middle letter does not stand out, so it is harder to recognize where the first half ends and the second half begins. In fact, it‘s not only harder; it's impossible
Palindrome Machine (even Palindrome)
Palindrome Machine (even Palindrome)
PDA accepts language from following CFG
Example
Assignment �Solve Question # of book 1, 2, 3, 5 at page 370
Another CFG to NPDA Example Equivalent PDA /NPDA is
Another CFG to NPDA Example Equivalent PDA /NPDA is
Another CFG to NPDA Example
Assignment �Solve Questions 1, 2, 3, 4, 5 at page 424
Chomsky Normal Form
Chomsky Normal Form
Chomsky Normal Form
- Pda theory of computation
- Pda
- Aab ccb
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