2. FINITESTATE AUNTOMATA WITH OUTPUTS
A FINITE STATE AUTOMATA WHICH CONTAINS BOTH THE INPUT AND THE OUTPUT THAT ARE GIVEN BY THE
AUTOMATA.
THERE ARE TWO TYPES OF MACHINES:
1. MEALY MACHINE:
A FINITE-STATE MACHINE WHOSE OUTPUT VALUES ARE DETERMINED BOTH BY ITS CURRENT STATE AND THE
CURRENT INPUT.
2. MOORE MACHINE:
A FINITE-STATE MACHINE WHOSE CURRENT OUTPUT VALUES ARE DETERMINED ONLY BY ITS CURRENT STATE.
3. MOORE MACHINE
MOORE MACHINE IS DEFINED USING SIX TUPLES .
(Q,Ʃ,Δ,𝛿,𝜆,𝑞0)
WHERE
Q= FINITE SET OF STATES
Ʃ= FINITE NON-EMPTY SET OF INPUT ALPHABETS
Δ=THE SET OF OUTPUT ALPHABETS
𝛿=TRANSITION FUNCTION: Q ×Ʃ Δ
𝜆= OUTPUT FUNCTION: Ʃ ×QΔ
𝑞0= INITIAL STATE/ START STATE
4. IN CASE OF MOORE MACHINE THE LENGTH OF OUR INPUT SYMBOL WAS 1 2 3 4
AND THE LENGTH OF THE OUTPUT STRING THAT IS PRODUCED WAS 1 2 3 4 5 SO
IN THIS CASE WE SEE THAT THE LENGTH IF THE LENGTH OF YOUR INPUTS STRING
IS N THE N THE LENGTH OF OUTPUT STRING IS ALWAYS N PLUS 1 OKAY THAT
WHEN WHY IS THAT THAT IS BECAUSE IN THE STARTING STATE THERE IS ALWAYS
AN OUTPUT ASSOCIATED WITH IT AND THAT IS ALWAYS PRINTED THAT IS WHY WE
HAVE THE LENGTH OF OUR OUTPUT STRING AS N PLUS 1 WHERE N IS THE NUMBER
OF STRINGS IN THE INPUT
5. NOW LET’S SEE THE EXAMPLES OF MEALY MACHINES:
EX: 1010
