1. COSC 3340: Introduction to Theory of Computation
University of Houston
Fall 2003, Dr. Verma
Lecture 11
Lecture 11
UofH - COSC Dr. Verma

2. Push Down Automaton (PDA)
Language Acceptor Model for CFLs
It is an NFA with a stack.
Finite
State
control
Input
Accept/Reject
Stack
Lecture 11
UofH - COSC Dr. Verma

3. PDA (contd.) In one move the PDA can :
change state,
consume a symbol from the input tape or ignore it
pop a symbol from the stack or ignore it
push a symbol onto the stack or not
A string is accepted provided the machine when started in the start state consumes the string and reaches a final state.
Lecture 11
UofH - COSC Dr. Verma

4. PDA (contd.)
If PDA in state q can consume u, pop x from stack, change state to p, and push w on stack we show it as
u, x  w q0 q1
u, x ; w
In JFLAP
Lecture 11
UofH - COSC Dr. Verma

5. Example of a PDA PDA L = {anbn |n  0}
Push S to the stack in the beginning and
then pop it at the end before accepting.
Lecture 11
UofH - COSC Dr. Verma

6. JFLAP Simulation
Lecture 11
UofH - COSC Dr. Verma

7. JFLAP Simulation
Lecture 11
UofH - COSC Dr. Verma

8. JFLAP Simulation
Lecture 11
UofH - COSC Dr. Verma

9. JFLAP Simulation
Lecture 11
UofH - COSC Dr. Verma

10. JFLAP Simulation
Lecture 11
UofH - COSC Dr. Verma

11. JFLAP Simulation
Lecture 11
UofH - COSC Dr. Verma

12. JFLAP Simulation
Lecture 11
UofH - COSC Dr. Verma

13. JFLAP Simulation
Lecture 11
UofH - COSC Dr. Verma

14. JFLAP Simulation
Lecture 11
UofH - COSC Dr. Verma

15. JFLAP Simulation
Lecture 11
UofH - COSC Dr. Verma

16. JFLAP Simulation
Lecture 11
UofH - COSC Dr. Verma

17. JFLAP Simulation
Lecture 11
UofH - COSC Dr. Verma

18. JFLAP Simulation
Lecture 11
UofH - COSC Dr. Verma

19. JFLAP Simulation
Lecture 11
UofH - COSC Dr. Verma

20. JFLAP Simulation
Lecture 11
UofH - COSC Dr. Verma

21. JFLAP Simulation
Lecture 11
UofH - COSC Dr. Verma

22. JFLAP Simulation
Lecture 11
UofH - COSC Dr. Verma

23. JFLAP Simulation
Lecture 11
UofH - COSC Dr. Verma

24. JFLAP Simulation
Lecture 11
UofH - COSC Dr. Verma

25. Definition of PDA Formally, a PDA M = (K, , , , s, F). where
K -- finite set of states
 -- is the input alphabet
 -- is the tape alphabet
s  K -- is the start state
F  K -- is the set of final states
  (K X  X ) X (K X )
Lecture 11
UofH - COSC Dr. Verma

26. Definition of L(M) Define * as:
(1) *(q, , ) = {(q, , )}  {(p, , ) |((q, , ), (p, ))  }
(2) *(q, uv, xy) = {(p, v, wy) | ((q, u, x), (p, w)) }
M accepts w if (f, , x) in *(s, w, )
L(M) = {w  * | M accepts w}
Lecture 11
UofH - COSC Dr. Verma

27. Example What is L(M)? Push S to the stack in the beginning and
then pop it at the end before accepting.
Lecture 11
UofH - COSC Dr. Verma