2way & with output automata

8/22/2019 2way & With Output Automata

1/25

TWO-WAYDETERMINISTIC

FINITE AUTOMATA

Presented By: Raushan kumar

(2DFA)


2/25

DFA

Input is processed once from left to right. After an

input has been read, the DFA decides whether the

input is accepted or rejected.

2DFA

Can read the input back and forth with no limit on how

many times an input symbol can be read.

As in the case of DFA, the 2DFA decides whether a given

input is accepted or rejected.


3/25

The concept of 2DFA was originated by Rabin and Scott

in 1997

2DFA is a generalized version of the DFA which can

revisit characters already processed.

WHATIS 2DFA?


4/25

HOW 2DFA WORKS?

Two-way Finite Automata have a read head, whichcan move left or right over the input string.

Consists of the symbols of the input string asoccupying cells of a finite tape, one symbol per cell.

The input string is enclosed in left and rightendmarkers and , which are not elements of theinput alphabet .

The read head may not move outside of theendmarkers.


5/25

STRUCTUREOF 2DFA


6/25

FORMAL DEFINITIONOF 2DFA

Is a quintuple

M = ( Q, , , q0 , F)

Function takes a state and a symbol asarguments and returns a new state and a direction

to move the head.

If (p, b) = (q, L/R), then whenever the machine is

in state p and scanning a tape cell containingsymbol b, it moves its head one cell in the direction

d and enters state q.


7/25

TURINGMACHINE

Move back and forth in the working tape while

reading and/or writing.

Has no limit to the amount of memory that it can

use.

2DFAs can be seen as read-only Turing machines with

no work tape, only a read-only input tape

EXAMPLE:


8/25

HOWDOES DFA COMPARETO 2DFA?

2DFA can solve any problems that are solvable by DFA.

Next, are there problems that can be solved by 2DFA but

cannot be solved by DFA


9/25

WHYNOT 2DFA?

Consumes less memory and time than DFA.

Problems that can be solved by DFA can be solved by

2DFA

Easy to implement/ much more powerful than DFA.


10/25

FINITEAUTOMATAWITHOUTPUT


11/25

MOOREAND MEALY MACHINES

Both these machine types follow the basic

characteristics of state machines, but differ in the

way that outputs are produced.

Moore Machine:

Outputs are independent of the inputs, ie outputs

are effectively produced from within the state of

the state machine.

Mealy Machine:

Outputs can be determined by the present state

and the present inputs, ie outputs are produced

as the machine makes a transition from one

state to another.


12/25

MATHEMATICAL

REPRESENTATION

M = (Q , , , , qo , )

Q = A nonempty finite set of state in M.

= A nonempty finite set of input symbols.

(delta.upp) = A nonempty finite set of outputs. (delta.low) = It is a transition function which

takes two arguments input state and inputsymbol.

qo

= Initial state of M belongs to Q. (lambda) = It is a mapping function which

maps Q to giving output associated with eachstate.


13/25

MOORE MACHINE DIAGRAMS

State 2

x,y

State 1

q,ra,b

i,j

Input condition that

must exist in order

to execute these

transitions from

State 1

Output condition that

results from being in

a particular present

state

The Moore State Machine

output is shown inside the

state bubble, because the

output remains the same as

long as the state machine

remains in that state.The output can be arbitrarily

complex but must be the

same every time the

machine enters that

state.


14/25

MOORE MACHINE

Describe Outputs as Concurrent Statements

Depending on State Only

state 1 /

output 1

state 2 /

output 2

transitioncondition 1

transition

condition 2


15/25

EXAMPLE OF

MOORE MACHINE

q0 q3 q1 0

q1 q1 q2 1

q2 q2 q3 0

q3 q3 q0 0

Present

state

input

a=0 a=1

output

TRANSITION TABLE


16/25

TRANSITION DIAGRAM

q0

q2 q3

q1

0

0

1

1

1

0

0 0

1

0

1

0

0


17/25

MEALY MACHINE DIAGRAMS

State 2

State 1

a,b

q,r

i,jx,y

Input condition that

must exist in order

to execute these

transitions from

State 1

Output condition that

results from being in

a particular present

state

The Mealy State Machinegenerates outputs based on:

The Present State, and

The Inputs to the M/c.

So, it is capable of generating

many different patterns of output

signals for the same state,

depending on the inputs present

on the clock cycle.

Outputs are shown on transitions

since they are determined in the

same way as is the next state.


18/25

MEALY MACHINE

Describe Outputs as Concurrent Statements

Depending on State and Inputs

state 1state 2

transition condition 1 /

output 1

transition condition 2 /

output 2


19/25

EXAMPLE OF

MEALY MACHINE

q1 q3 0 q2 0

q2 q1 1 q4 1

q3 q2 1 q1 0

q4 q4 1 q3 0

Present

state

Input a = 0

State output

Input a = 1

Stateoutput

TRANSITION TABLE


20/25

q1

q3 q4

q2

TRANSITION DIAGRAM

1/1

0/1

0/1

1/0

1/0 0/0

1/0

0/1


21/25

TRANSFORMING A MOORE MACHINE INTO

A MEALY MACHINE

q1

q1MOOREMACHINE

MEALY

MACHINE

d

c/P

b/P

a/P

d

P

c

b

a


22/25

EXAMPLE

q0 q3

q2

q1

0 1

0

1

MOORE MACHINE

aa

a

a/b

b

b

b


23/25

CONVERT INTO MEALY MACHINE

q0 q3

q2

q1

MEALY MACHINE

a/1 , b/1

a/1a/1

b/0

b/0b/1

a/0


24/25

TRANSFORMING A MEALY MACHINE INTO

A MOORE MACHINE

q1

q11 q12

10

ba

a/1

a/1

b/1 b/1

MOORE MACHINE

MEALY MACHINE

b/0

a/0

a/1

b/1 b/1

b


25/25

THANK YOU

2way & with output automata

Documents