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

Lecture 11 UofH - COSC 3340 - Dr. Verma1

COSC 3340: Introduction to Theory of Computation

University of Houston

Dr. Verma

Lecture 11

Lecture 11 UofH - COSC 3340 - Dr. Verma2

Push Down Automaton (PDA)

Language Acceptor Model for CFLs It is an NFA with a stack.

Finite State

controlInput

Stack

Accept/Reject

Lecture 11 UofH - COSC 3340 - Dr. Verma3

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 3340 - Dr. Verma4

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

q0

u, x w

q1

u, x ; w In JFLAP

Lecture 11 UofH - COSC 3340 - Dr. Verma5

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 3340 - Dr. Verma6

JFLAP Simulation

Lecture 11 UofH - COSC 3340 - Dr. Verma7

JFLAP Simulation

Lecture 11 UofH - COSC 3340 - Dr. Verma8

JFLAP Simulation

Lecture 11 UofH - COSC 3340 - Dr. Verma9

JFLAP Simulation

Lecture 11 UofH - COSC 3340 - Dr. Verma10

JFLAP Simulation

Lecture 11 UofH - COSC 3340 - Dr. Verma11

JFLAP Simulation

Lecture 11 UofH - COSC 3340 - Dr. Verma12

JFLAP Simulation

Lecture 11 UofH - COSC 3340 - Dr. Verma13

JFLAP Simulation

Lecture 11 UofH - COSC 3340 - Dr. Verma14

JFLAP Simulation

Lecture 11 UofH - COSC 3340 - Dr. Verma15

JFLAP Simulation

Lecture 11 UofH - COSC 3340 - Dr. Verma16

JFLAP Simulation

Lecture 11 UofH - COSC 3340 - Dr. Verma17

JFLAP Simulation

Lecture 11 UofH - COSC 3340 - Dr. Verma18

JFLAP Simulation

Lecture 11 UofH - COSC 3340 - Dr. Verma19

JFLAP Simulation

Lecture 11 UofH - COSC 3340 - Dr. Verma20

JFLAP Simulation

Lecture 11 UofH - COSC 3340 - Dr. Verma21

JFLAP Simulation

Lecture 11 UofH - COSC 3340 - Dr. Verma22

JFLAP Simulation

Lecture 11 UofH - COSC 3340 - Dr. Verma23

JFLAP Simulation

Lecture 11 UofH - COSC 3340 - Dr. Verma24

JFLAP Simulation

Lecture 11 UofH - COSC 3340 - Dr. Verma25

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 3340 - Dr. Verma26

Definition of L(M)

Define * as:(1) *(q, , ) = {(q, , )} {(p, , ) |((q, , ), (p, )) }

(2) *(q, uv, xy) = U {*(p, v, wy) | ((q, u, x), (p, w)) }

i.e., first compute * for all successor configurations and then take the union of all those sets

M accepts w if (f, , x) in *(s, w, ) Alternative: if (f, , ) in *(s, w, ) [we use] L(M) = {w * | M accepts w}

Lecture 11 UofH - COSC 3340 - Dr. Verma27

Example

What is L(M)?

Push S to the stack in the beginning and then pop it at the end before accepting.