Pushdown AutomataA NEW FORM OF FA’S

Terms To Know:

Input Tape

Pictorial Representation

Start

Reject

Accept

Read

Example

Stack

Pushdown Automata

Input Tape

The Part of FA where the input lives is called Input Tape

The Location is which we put input letter is called cells

Example Of Input Tape

The Example of tape that contain some of our input letter

Here ∆ is used to indicate the blank in the tape cell

Means that this cell is empty and we can place a letter into this cell

Input Tape: Properties

As we process the tape onto the machine

We read one letter a time

After reading the letter we will eliminate that letter assuming that it is used

When we will read first blank cell we will stop because we will assume that after first blank cell all other cells will also be blank

And we read cells from Left To Right

Start / Reject / Accept

A start State is a state from where we begin the process but read inputs no letter

A start state has no arrow coming into it

A reject state Is dead-end non final state, where all the input is consumed but we did not achieve the goal

A Accept state is a dead-end a final state tells that the input is accepted and we have achieved our goal

Start

Reject

Accept

Read State

We are changing our diagrams so an important thing in our FA’s was to read a letter and then decide where to go so in pictorial representation we have introduced a READ state.

Read state is just like a diamond shape.

Remember

When the character ∆ is read from input tape means that we are out of input

Then we Finish Processing

The ∆-edge will lead us to accept state if the state have stop into final

Other wise it will lead us to reject state

In old methods we have no idea when we are out of inputs

Example: Convert FA to Pictorial Representation:

What is the benefit????

It just like flow chart so what is the reason to use this and

Using Pictorial representation we still representation the FA’s so how can we give more power to our machine?????

For this purpose we will use the “STACK”

It is easy to use stack with these pictorial representation

Stack: Push Down Stack/ Push Down Store

A stack is a storage point where we can store our input letter

And then call them back when we will refer it

Stack Pointer: That point the top of the stack

It has two main Operations

Push

POP

PDA: Push Down Automata

When FA’s have been souped up with the

Stack

Push

Pop

Then we call it the push down automata abbreviated as PDA’s

By adding this data structure the language recognizing capability is increased.

How To Define a PDA

A push down automata is collection of 8 things

An alphabet ∑ (Segma)of input letters

An input Tape

An Alphabet (Taa) of stack character

A pushdown stack

On start State

Halt States

Push State

Read State

State Read Top of stack